Quick Answer
Practice questions for SAT linear inequalities in one variable assess your ability to solve, graph, and interpret inequalities involving a single variable, such as absolute value inequalities, compound inequalities, and real-world constraint models. There are 65 SAT-style linear inequality questions on this website, along with full solutions, answer options, and trap notes. Beginning with simple inequality solutions, the questions progress to more difficult mixed reasoning issues, word problems, compound inequalities, and equivalent forms.
What to Know Before You Start
- A linear inequality in one variable compares an expression to a value using <, >, ≤, or ≥ instead of an equals sign.
- Flip the inequality sign whenever you multiply or divide both sides by a negative number.
- Usually shown as a shaded area on a number line or expressed in interval notation, solutions to an inequality are a range of values rather than a single number.
- Compound inequalities (such as 3 < x + 1 ≤ 9) describe two conditions at once and are solved by working on all parts together.
- In word problems, phrases like “at least,” “at most,” “no more than,” and “exceeds” signal which inequality symbol to use.
- Forgetting to reverse the sign, confusing “at least” with “at most,” or solving as if the inequality were an equation and stopping early are all common causes of incorrect responses.
In This Guide – 65 Linear Inequalities Practice Questions
- What does the SAT test in linear inequalities?
- How do SAT questions test basic inequality solving?
- How do you handle compound and absolute value inequalities?
- How are inequalities used in SAT word problems?
- How do you move between forms and graphs of inequalities?
- What do hard SAT inequality questions look like?
- What mistakes cost students points on inequalities?
- How should you study SAT inequalities in 2 weeks?
- Frequently asked questions
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What Does the SAT Test in Linear Inequalities?
One-variable linear inequalities fall under the SAT Math Algebra area. They could show up on the Digital SAT as a direct inequality to answer, a compound inequality, a real-world limitation (such as a budget, a weight limit, or a minimum score), or a question regarding which graph or interval corresponds with a certain inequality. The language frequently determines whether you choose the right direction of the inequality, but the algebra is rarely lengthy.
Prior to solution, a proficient SAT student determines the variable, the boundary value, and whether the boundary is included (≤, ≥) or excluded. (<, >). Most inequality questions become quick algebra problems rather than perplexing word problems if those three components are understood.
| Inequality Skill | What It Tests | Common Trap | Practice Set |
|---|---|---|---|
| Basic solving | Isolating the variable, sign flips | Forgetting to flip the sign | Q1–Q15 |
| Compound & absolute value | Two-sided inequalities, |x| forms | Only solving one side | Q16–Q30 |
| Word problems | Translating constraints into inequalities | Wrong direction of inequality | Q31–Q45 |
| Forms & graphs | Interval notation, number lines, matching graphs | Open vs. closed circle confusion | Q46–Q55 |
| Hard mixed | Parameters, systems, multi-step reasoning | Solving before understanding the constraint | Q56–Q65 |
SAT strategy: Before solving, ask: What is being compared? Is the boundary value included? Will I need to flip the sign at any step?
How Do SAT Questions Test Basic Inequality Solving?
One-step and two-step inequalities should be used first. These questions test your ability to isolate the variable and recall to flip the sign when necessary.
Basic Inequality Solving · Easy · Question 1
Solve for x: 3x + 5 < 20
A) x < 5
B) x > 5
C) x < 25
D) x > 25/3
Show full solution
3x < 15, so x < 5. Answer: A
Basic Inequality Solving · Easy · Question 2
Solve for x: -2x + 4 ≥ 10
A) x ≥ -3
B) x ≤ -3
C) x ≥ 3
D) x ≤ 3
Show full solution
-2x ≥ 6, divide by -2 and flip: x ≤ -3. Answer: B
Basic Inequality Solving · Easy · Question 3
Solve for x: (x/4) – 3 > 1
A) x > 4
B) x > 8
C) x > 16
D) x > 12
Show full solution
x/4 > 4, so x > 16. Answer: C
Basic Inequality Solving · Medium · Question 4
Solve for x: 5 – 2x ≤ 17
A) x ≤ -6
B) x ≥ -6
C) x ≥ 6
D) x ≤ 6
Show full solution
-2x ≤ 12, divide by -2 and flip: x ≥ -6. Answer: B
Basic Inequality Solving · Medium · Question 5
Solve for x: 3(x – 2) > 2(x + 1)
A) x > 8
B) x > -8
C) x < 8
D) x > 4
Show full solution
3x – 6 > 2x + 2, so x > 8. Answer: A
Basic Inequality Solving · Easy · Question 6
Which value of x does NOT satisfy 2x – 3 ≤ 9?
A) 4
B) 6
C) 7
D) 5
Show full solution
2x ≤ 12, so x ≤ 6. x = 7 fails. Answer: C
Basic Inequality Solving · Medium · Question 7
Solve for x: -(x/3) + 2 < 5
A) x > -9
B) x < -9
C) x > 9
D) x < 9
Show full solution
-x/3 < 3, multiply by -3 and flip: x > -9. Answer: A
Basic Inequality Solving · Medium · Question 8
If 4x – 7 ≥ 2x + 9, what is the smallest integer value of x?
A) 7
B) 8
C) 9
D) 6
Show full solution
2x ≥ 16, so x ≥ 8. Smallest integer: 8. Answer: B
Basic Inequality Solving · Easy · Question 9
Solve for x: 7x ≤ 4x – 12
A) x ≤ -4
B) x ≥ -4
C) x ≤ 4
D) x ≥ 4
Show full solution
3x ≤ -12, so x ≤ -4. Answer: A
Basic Inequality Solving · Hard · Question 10
If -3(2 – x) > 5x – 4, what is the solution set?
A) x > -1
B) x < -1
C) x > 1
D) x < 1
Show full solution
-6 + 3x > 5x – 4, so -2 > 2x, x < -1. Answer: B
Basic Inequality Solving · Easy · Question 11
Solve for x: 6 < x + 2
A) x < 4
B) x > 4
C) x > 8
D) x < 8
Show full solution
4 < x, which is the same as x > 4. Answer: B
Basic Inequality Solving · Easy · Question 12
Solve for x: -4x > 20
A) x > -5
B) x < -5
C) x > 5
D) x < 5
Show full solution
Divide by -4 and flip: x < -5. Answer: B
Basic Inequality Solving · Medium · Question 13
If 2(x + 3) ≥ 4x – 2, what is the largest integer that satisfies the inequality if x must also be less than 5?
A) 4
B) 5
C) 3
D) 6
Show full solution
2x + 6 ≥ 4x – 2, so 8 ≥ 2x, x ≤ 4. Combined with x < 5, the largest integer is 4. Answer: A
Basic Inequality Solving · Medium · Question 14
Solve for x: (2x – 1)/3 > 5
A) x > 8
B) x > 7
C) x > 16
D) x > 6
Show full solution
2x – 1 > 15, so 2x > 16, x > 8. Answer: A
Basic Inequality Solving · Hard · Question 15
If 0.5x – 3 ≤ 1.5x + 1, what is the solution set?
A) x ≥ -4
B) x ≤ -4
C) x ≥ 4
D) x ≤ 4
Show full solution
-4 ≤ x, which is the same as x ≥ -4. Answer: A
Do You Need a Quicker Plan to Raise Your SAT Math Score?
When practice questions are linked to a weekly score strategy, they are most beneficial. Use TestPrepKart’s SAT preparation tools for personalised math practice, error review, live instruction, and mock exams.
When practice questions are linked to a weekly score strategy, they are most beneficial. Use TestPrepKart’s SAT preparation tools for personalised math practice, error review, live instruction, and mock exams.
How Do You Handle Compound and Absolute Value Inequalities on the SAT?
These questions focus on two-sided inequalities, absolute value inequalities, and combining conditions correctly.
Compound & Absolute Value · Easy · Question 16
Solve for x: -3 < x – 2 < 4
A) -1 < x < 6
B) -5 < x < 2
C) -1 < x < 2
D) -5 < x < 6
Show full solution
Add 2 to all three parts: -1 < x < 6. Answer: A
Compound & Absolute Value · Medium · Question 17
Solve for x: 5 ≤ 2x + 1 ≤ 13
A) 2 ≤ x ≤ 6
B) 3 ≤ x ≤ 7
C) 2 ≤ x ≤ 7
D) 4 ≤ x ≤ 6
Show full solution
Subtract 1: 4 ≤ 2x ≤ 12. Divide by 2: 2 ≤ x ≤ 6. Answer: A
Compound & Absolute Value · Medium · Question 18
Solve for x: |x – 4| < 6
A) -2 < x < 10
B) -10 < x < 2
C) -6 < x < 6
D) 2 < x < 10
Show full solution
-6 < x – 4 < 6, so -2 < x < 10. Answer: A
Compound & Absolute Value · Medium · Question 19
Solve for x: |2x + 3| ≥ 9
A) x ≤ -6 or x ≥ 3
B) x ≤ -3 or x ≥ 6
C) -6 ≤ x ≤ 3
D) -3 ≤ x ≤ 6
Show full solution
2x + 3 ≥ 9 gives x ≥ 3. 2x + 3 ≤ -9 gives x ≤ -6. Answer: A
Compound & Absolute Value · Easy · Question 20
Which value of x does NOT satisfy -4 ≤ x < 5?
A) -4
B) 0
C) 5
D) 4
Show full solution
The upper bound 5 is excluded (strict <). Answer: C
Compound & Absolute Value · Medium · Question 21
Solve for x: |x + 1| ≤ 3
A) -4 ≤ x ≤ 2
B) -2 ≤ x ≤ 4
C) -3 ≤ x ≤ 3
D) -1 ≤ x ≤ 3
Show full solution
-3 ≤ x + 1 ≤ 3, so -4 ≤ x ≤ 2. Answer: A
Compound & Absolute Value · Hard · Question 22
Solve for x: -2 < -x + 3 < 5
A) -2 < x < 5
B) -5 < x < 2
C) 5 < x < -2
D) 2 < x < 5
Show full solution
Subtract 3: -5 < -x < 2. Divide by -1 and flip both: 5 > x > -2, i.e., -2 < x < 5. Answer: A
Compound & Absolute Value · Medium · Question 23
Solve for x: |3x| > 12
A) x > 4 or x < -4
B) -4 < x < 4
C) x > 4
D) x < -4
Show full solution
3x > 12 or 3x < -12, so x > 4 or x < -4. Answer: A
Compound & Absolute Value · Medium · Question 24
Which compound inequality describes all values of x within 5 units of 8?
A) |x – 8| ≤ 5
B) |x + 8| ≤ 5
C) |x – 5| ≤ 8
D) |x| ≤ 13
Show full solution
“Within 5 units of 8” means the distance from x to 8 is at most 5. Answer: A
Compound & Absolute Value · Medium · Question 25
Solve for x: 2 < 3 – x ≤ 7
A) -4 ≤ x < 1
B) 1 ≤ x < -4
C) -4 < x ≤ 1
D) 1 < x ≤ -4
Show full solution
Subtract 3: -1 < -x ≤ 4. Divide by -1 and flip: 1 > x ≥ -4, i.e., -4 ≤ x < 1. Answer: A
Compound & Absolute Value · Hard · Question 26
Solve for x: |4x – 2| < 10
A) -2 < x < 3
B) -3 < x < 2
C) -2 < x < 2
D) -3 < x < 3
Show full solution
-10 < 4x – 2 < 10, so -8 < 4x < 12, giving -2 < x < 3. Answer: A
Compound & Absolute Value · Easy · Question 27
Which number line correctly shows -1 < x ≤ 4?
A) Open circle at -1, closed circle at 4, shaded between
B) Closed circle at -1, open circle at 4, shaded between
C) Open circles at both -1 and 4, shaded between
D) Closed circles at both -1 and 4, shaded between
Show full solution
< means an open (excluded) circle at -1; ≤ means a closed (included) circle at 4. Answer: A
Compound & Absolute Value · Medium · Question 28
Solve for x: |x/2 – 1| ≤ 3
A) -4 ≤ x ≤ 8
B) -8 ≤ x ≤ 4
C) -2 ≤ x ≤ 4
D) -6 ≤ x ≤ 6
Show full solution
-3 ≤ x/2 – 1 ≤ 3, so -2 ≤ x/2 ≤ 4, giving -4 ≤ x ≤ 8. Answer: A
Compound & Absolute Value · Hard · Question 29
For which values of x is |x – 6| > 2 true?
A) x < 4 or x > 8
B) 4 < x < 8
C) x < 4
D) x > 8
Show full solution
x – 6 > 2 or x – 6 < -2, so x > 8 or x < 4. Answer: A
Compound & Absolute Value · Medium · Question 30
Solve for x: -6 ≤ 2x – 4 < 10
A) -1 ≤ x < 7
B) -5 ≤ x < 3
C) -1 ≤ x < 3
D) 1 ≤ x < 7
Show full solution
Add 4: -2 ≤ 2x < 14. Divide by 2: -1 ≤ x < 7. Answer: A
How Are Linear Inequalities Used in SAT Word Problems?
In SAT word problems, phrases like “at least,” “at most,” “no more than,” and “greater than” tell you which symbol to use. Translate the sentence into an inequality before solving.
Word Problems · Easy · Question 31
A school event costs $150 to set up plus $8 per attendee. The organizer has a budget of at most $500. Which inequality gives the possible number of attendees a?
A) 150 + 8a ≤ 500
B) 150 + 8a ≥ 500
C) 8 + 150a ≤ 500
D) 150a + 8 ≤ 500
Show full solution
“At most $500” means total cost ≤ 500, and total cost is 150 + 8a. Answer: A
Word Problems · Medium · Question 32
Using the event from Question 31, what is the maximum number of attendees allowed?
A) 40
B) 43
C) 44
D) 50
Show full solution
8a ≤ 350, so a ≤ 43.75. Since attendees must be a whole number, the maximum is 43. Answer: B
Word Problems · Easy · Question 33
A student needs a total score of at least 350 points across two tests. She scored 160 on the first test. Which inequality gives the possible scores s on the second test?
A) s ≥ 190
B) s ≤ 190
C) s ≥ 510
D) s ≥ 350
Show full solution
160 + s ≥ 350, so s ≥ 190. Answer: A
Word Problems · Medium · Question 34
A moving truck can carry no more than 3,000 pounds. Each box weighs 40 pounds and the driver weighs 180 pounds. Which inequality gives the possible number of boxes b?
A) 40b + 180 ≤ 3000
B) 40b + 180 ≥ 3000
C) 180b + 40 ≤ 3000
D) 40b ≤ 180
Show full solution
“No more than” means ≤. Total weight is 40b + 180. Answer: A
Word Problems · Medium · Question 35
Using the truck from Question 34, what is the maximum number of boxes it can carry?
A) 68
B) 70
C) 71
D) 79
Show full solution
40b ≤ 2820, so b ≤ 70.5. Maximum whole number of boxes: 70. Answer: B
Word Problems · Easy · Question 36
A parking garage charges $5 for the first hour and $3 for each additional hour. Which inequality describes the number of additional hours h if the total charge must stay under $20?
A) 5 + 3h < 20
B) 3 + 5h < 20
C) 5 + 3h ≤ 20
D) 5h + 3 < 20
Show full solution
“Under $20” means strictly less than 20. Total charge is 5 + 3h. Answer: A
Word Problems · Medium · Question 37
A company must produce at least 200 units per day but has capacity for at most 350 units. Which inequality represents the possible daily production p?
A) 200 ≤ p ≤ 350
B) 200 < p < 350
C) p ≤ 200 or p ≥ 350
D) p ≥ 550
Show full solution
“At least” and “at most” both include the boundary. Answer: A
Word Problems · Medium · Question 38
A gym membership costs $30 per month with no sign-up fee. A competing gym costs $50 per month but includes free classes. After how many months does the second gym cost more than the first, given the difference must exceed $120?
A) more than 6 months
B) more than 5 months
C) more than 4 months
D) more than 8 months
Show full solution
50m – 30m > 120, so 20m > 120, m > 6. Answer: A
Word Problems · Easy · Question 39
A recipe requires the oven temperature to stay between 325°F and 375°F, inclusive. Which inequality represents the allowed temperature T?
A) 325 ≤ T ≤ 375
B) 325 < T < 375
C) T ≤ 325 or T ≥ 375
D) 325 ≤ T < 375
Show full solution
“Inclusive” means both endpoints are included. Answer: A
Word Problems · Medium · Question 40
A salesperson earns $400 per week plus $25 per sale. To earn more than $650 in a week, how many sales are needed at minimum?
A) 11
B) 10
C) 12
D) 9
Show full solution
400 + 25s > 650, so 25s > 250, s > 10. The minimum whole number of sales is 11. Answer: A
Word Problems · Medium · Question 41
A charity needs to raise at least $2,400. So far $900 has been raised, and each additional donor gives $60. Which inequality gives the minimum number of additional donors d needed?
A) d ≥ 25
B) d ≥ 20
C) d ≥ 30
D) d ≥ 40
Show full solution
900 + 60d ≥ 2400, so 60d ≥ 1500, d ≥ 25. Answer: A
Word Problems · Easy · Question 42
A container can hold at most 45 liters. It already has 12 liters. Which inequality gives the amount x that can still be added?
A) x ≤ 33
B) x ≥ 33
C) x ≤ 45
D) x ≤ 57
Show full solution
12 + x ≤ 45, so x ≤ 33. Answer: A
Word Problems · Hard · Question 43
Plan A costs $10 plus $0.05 per minute. Plan B costs $25 with unlimited minutes. For how many minutes does Plan A cost more than Plan B?
A) more than 300 minutes
B) more than 250 minutes
C) more than 350 minutes
D) more than 200 minutes
Show full solution
10 + 0.05m > 25, so 0.05m > 15, m > 300. Answer: A
Word Problems · Medium · Question 44
A student has read 45 pages of a 300-page book and plans to read 25 pages per day. What is the minimum number of days needed to have read at least 220 pages total?
A) 7
B) 8
C) 6
D) 9
Show full solution
45 + 25d ≥ 220, so 25d ≥ 175, d ≥ 7. Answer: A
Word Problems · Medium · Question 45
A theater seats no more than 220 people. If 85 seats are already reserved, which inequality gives the number of additional tickets t that can be sold?
A) t ≤ 135
B) t ≥ 135
C) t ≤ 220
D) t ≤ 305
Show full solution
85 + t ≤ 220, so t ≤ 135. Answer: A
Need a Faster SAT Math Score Improvement Plan?
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How Do You Move Between Forms and Graphs of Linear Inequalities?
The SAT often gives the same inequality in different forms — interval notation, a number line, or a rearranged expression. You may need to translate between them.
Forms & Graphs · Easy · Question 46
Which interval notation represents x ≥ -3?
A) [-3, ∞)
B) (-3, ∞)
C) (-∞, -3]
D) (-∞, -3)
Show full solution
≥ includes the boundary, shown with a square bracket: [-3, ∞). Answer: A
Forms & Graphs · Easy · Question 47
Which inequality is represented by the interval (2, 9]?
A) 2 < x ≤ 9
B) 2 ≤ x < 9
C) 2 ≤ x ≤ 9
D) 2 < x < 9
Show full solution
A parenthesis excludes the endpoint; a bracket includes it. Answer: A
Forms & Graphs · Medium · Question 48
Which inequality is equivalent to 2(x – 3) ≤ 4x + 2?
A) x ≥ -4
B) x ≤ -4
C) x ≥ 4
D) x ≤ 4
Show full solution
2x – 6 ≤ 4x + 2, so -8 ≤ 2x, x ≥ -4. Answer: A
Forms & Graphs · Medium · Question 49
Which graph description matches x < -2 or x > 5?
A) Two open circles at -2 and 5, shaded outward in both directions
B) Two closed circles at -2 and 5, shaded outward in both directions
C) Open circles at -2 and 5, shaded between them
D) One open circle at -2, shaded to the right only
Show full solution
Strict inequalities use open circles, and “or” means the two rays point away from each other. Answer: A
Forms & Graphs · Hard · Question 50
Which inequality is equivalent to -5x + 10 > 0?
A) x < 2
B) x > 2
C) x < -2
D) x > -2
Show full solution
-5x > -10, divide by -5 and flip: x < 2. Answer: A
Forms & Graphs · Medium · Question 51
Which interval notation represents -6 < x < -1?
A) (-6, -1)
B) [-6, -1]
C) (-6, -1]
D) [-6, -1)
Show full solution
Both inequalities are strict, so both endpoints use parentheses. Answer: A
Forms & Graphs · Hard · Question 52
A number line shows a closed circle at 3 shaded to the left. Which inequality matches the graph?
A) x ≤ 3
B) x < 3
C) x ≥ 3
D) x > 3
Show full solution
A closed circle includes the boundary, and shading left means values less than or equal to 3. Answer: A
Forms & Graphs · Medium · Question 53
Which inequality is equivalent to (x + 4)/2 ≥ 3?
A) x ≥ 2
B) x ≤ 2
C) x ≥ 6
D) x ≥ -2
Show full solution
x + 4 ≥ 6, so x ≥ 2. Answer: A
Forms & Graphs · Hard · Question 54
Which inequality has the same solution set as -3(x – 1) < 2x + 13?
A) x > -2
B) x < -2
C) x > 2
D) x < 2
Show full solution
-3x + 3 < 2x + 13, so -10 < 5x, x > -2. Answer: A
Forms & Graphs · Medium · Question 55
Which pair of inequalities has the same solution set as -2 ≤ x + 1 ≤ 6?
A) x ≥ -3 and x ≤ 5
B) x ≥ -1 and x ≤ 7
C) x ≥ -3 and x ≤ 7
D) x ≥ 3 and x ≤ 5
Show full solution
Subtract 1 from all parts: -3 ≤ x ≤ 5. Answer: A
What Do Hard SAT Linear Inequality Questions Look Like?
Harder questions combine compound inequalities, parameters, systems of inequalities, and real-world interpretation. The algebra is still linear, but the setup takes more careful reading.
Hard Mixed · Hard · Question 56
If 3 < 2x – 1 and 2x – 1 < 11, what is the complete solution set for x?
A) 2 < x < 6
B) 1 < x < 5
C) 2 < x < 5
D) 1 < x < 6
Show full solution
Combine into 3 < 2x – 1 < 11. Add 1: 4 < 2x < 12. Divide by 2: 2 < x < 6. Answer: A
Hard Mixed · Hard · Question 57
If kx – 4 > 10 has the solution x > 7, what is the value of k?
A) 2
B) 3
C) 4
D) 5
Show full solution
kx > 14, so x > 14/k. Setting 14/k = 7 gives k = 2 (positive k keeps the inequality direction unchanged). Answer: A
Hard Mixed · Hard · Question 58
A number n satisfies both n + 5 > 12 and 3n ≤ 27. What is the complete solution set for n?
A) 7 < n ≤ 9
B) 7 ≤ n < 9
C) 7 < n < 9
D) n > 9
Show full solution
n > 7 from the first inequality; n ≤ 9 from the second. Combined: 7 < n ≤ 9. Answer: A
Hard Mixed · Hard · Question 59
If |x – 3| > 4 and x must also be less than 10, what integer values satisfy both conditions?
A) x < -1 or 7 < x < 10
B) -1 < x < 7
C) x < 7
D) x > -1
Show full solution
|x – 3| > 4 gives x > 7 or x < -1. Combined with x < 10, the second branch becomes 7 < x < 10. Answer: A
Hard Mixed · Hard · Question 60
Plan A costs $15 plus $0.08 per text. Plan B costs $5 plus $0.20 per text. For how many texts does Plan A cost less than Plan B?
A) more than about 83 texts
B) fewer than about 83 texts
C) more than 100 texts
D) fewer than 50 texts
Show full solution
15 + 0.08t < 5 + 0.20t, so 10 < 0.12t, t > 83.3. Answer: A
Hard Mixed · Hard · Question 61
If -2 ≤ 3 – x ≤ 8, what is the greatest possible value of 2x?
A) 10
B) 5
C) -10
D) 16
Show full solution
Subtract 3: -5 ≤ -x ≤ 5. Divide by -1 and flip: 5 ≥ x ≥ -5, so -5 ≤ x ≤ 5. Greatest x is 5, so greatest 2x is 10. Answer: A
Hard Mixed · Medium · Question 62
If a > b and both are multiplied by -1, which statement is true?
A) -a < -b
B) -a > -b
C) -a = -b
D) It cannot be determined
Show full solution
Multiplying both sides of an inequality by a negative number flips the direction. Answer: A
Hard Mixed · Hard · Question 63
If ax + b < 0 has the solution x > -3, and a is negative, which could be the values of a and b?
A) a = -2, b = -6
B) a = -2, b = 6
C) a = 2, b = -6
D) a = 2, b = 6
Show full solution
With a = -2, b = -6: -2x – 6 < 0 gives -2x < 6, and dividing by -2 (flip) gives x > -3. Answer: A
Hard Mixed · Hard · Question 64
A number x satisfies 2x + 1 > 9 and also 5x – 2 < 28. What is the complete solution set?
A) 4 < x < 6
B) 4 < x < 5
C) x > 4
D) x < 6
Show full solution
First inequality: 2x > 8, so x > 4. Second inequality: 5x < 30, so x < 6. Combined: 4 < x < 6. Answer: A
Hard Mixed · Hard · Question 65
A student says that 4x – 8 < 0 and x < 2 are different because the first has more terms. Which explanation is correct?
A) They are the same because dividing 4x < 8 by 4 gives x < 2.
B) They are different because the second has no coefficient.
C) They are the same only when x = 0.
D) They are different because the direction of the inequality changes.
Show full solution
Adding 8 and dividing by a positive number (4) does not flip the inequality, so both forms describe the same solution set. Answer: A
Need a Faster SAT Math Score Improvement Plan?
Practice questions help most when they are connected to a weekly score plan. Use TestPrepKart SAT prep support for live classes, mock tests, error review, and targeted math practice.
What Mistakes Cost Students Points on SAT Linear Inequalities?
| Mistake | Why It Hurts | What to Do Instead |
|---|---|---|
| Forgetting to flip the sign | Multiplying or dividing by a negative number reverses the inequality. | Flip the symbol any time you multiply or divide by a negative. |
| Mixing up “at least” and “at most” | “At least” means ≥ and “at most” means ≤ — reversing them flips the answer. | Translate the phrase into a symbol before writing the inequality. |
| Treating the boundary as excluded or included incorrectly | ≤ and ≥ include the boundary; < and > do not. | Check whether the symbol has a line under it before graphing or answering. |
| Ignoring that answers must be whole numbers | Word problems about people, boxes, or tickets need whole-number answers. | Round to the nearest valid whole number in the correct direction. |
| Solving only one branch of an absolute value inequality | Absolute value inequalities usually split into two conditions. | Write both cases (positive and negative) before solving. |
How Should You Study SAT Linear Inequalities in 2 Weeks?
| Days | Focus | What to Practice |
|---|---|---|
| Days 1–2 | Basic solving | Isolate the variable and practice flipping the sign correctly. |
| Days 3–5 | Compound and absolute value | Solve two-sided inequalities and split absolute value inequalities into two cases. |
| Days 6–8 | Word problems | Translate “at least,” “at most,” and “no more than” into inequalities. |
| Days 9–11 | Forms and graphs | Convert between inequality notation, interval notation, and number lines. |
| Days 12–14 | Timed mixed review | Do 20 mixed inequality questions, review every missed setup, and retest. |
How Did Students Improve on SAT Linear Inequality Questions?
Case Study 1: Grade 10 student in Fremont, California
This student could solve basic inequalities, but she frequently lost points on word problems because she was unable to determine whether a phrase implied ≤ or ≥. We developed her strategy based on turning significant phrases into symbols before creating any calculations. After ten days of concentrated inequity practice, her accuracy on SAT Algebra questions rose from 60% to 85% in timed exercises.
Case Study 2: Grade 11 student in Edison, New Jersey
This student repeatedly failed to flip the inequality sign when dividing by a negative number, even though they had a solid algebraic foundation. We made sure he double-checked the direction after teaching him to highlight the sign each time he split. After three weeks, he stopped missing sign-flip questions and became more consistent when it came to compound inequality problems.
Frequently Asked Questions About Linear Inequalities in One Variable
Are linear inequalities important on the SAT?
Indeed.They often appear in the subject of algebra as word problems from everyday life as well as direct-solving problems..
What is the fastest way to solve SAT linear inequality questions?
Every time you multiply or divide by a negative integer, keep in mind to invert the inequality sign and isolate the variable exactly as you would in an equation.
How do I know when to flip the inequality sign?
The sign will only be reversed if you divide or multiply both sides by a negative number. Adding, subtracting, or multiplying by a positive integer never flips it. .
What is the difference between a compound inequality and an absolute value inequality?
A compound inequality directly states two conditions, such as 3 < x + 1 ≤ 9. An absolute value inequality, such as |x – 3| < 4, must first be rewritten as a compound inequality before solving.
Can Desmos help with SAT linear inequalities?
Yes. Graphing the shaded region for an inequality on Desmos can help determine the accuracy of a solution set, especially for compound and absolute value inequalities..
How many linear inequality questions should I practice before the SAT?
Before the test, the majority of students benefit from completing 60–80 mixed practice questions that cover word problems, compound inequalities, basic solutions, and graph interpretation.
Need a Faster SAT Math Score Improvement Plan?
Practice questions help most when they are connected to a weekly score plan. Use TestPrepKart SAT prep support for live classes, mock tests, error review, and targeted math practice.
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