The rules that solve most questions
- Isolate x exactly as you would in an equation.
- Flip the sign (< becomes >) whenever you multiply or divide both sides by a negative number.
- To check a choice, substitute it into the original inequality.
- A strict inequality (< or >) excludes the boundary value; ≤ and ≥ include it.
Traps the wrong answers are built on
- Forgetting to flip the sign after dividing by a negative.
- Choosing the boundary value itself for a strict inequality.
Worked example
Which of the following values of x satisfies the inequality 2x − 3 < 5?
- A. 8
- B. 5
- C. 4
- D. 3
Answer: D. Subtract −3 from both sides: 2x < 8. Divide by 2: x < 4. Only 3 is less than 4. (x = 4 itself makes the two sides equal, so it doesn't work.)
Practice set
Answer each question to see whether you're right and why. When you finish, draw a new set: the numbers change every time.
0 of 10 answered · 0 correct · set 1
- Question 1Easier
Which of the following values of x satisfies the inequality 2x − 3 < 5?
Show answer and explanation
Answer: D
Subtract −3 from both sides: 2x < 8.
Divide by 2: x < 4.
Only 3 is less than 4. (x = 4 itself makes the two sides equal, so it doesn't work.)
- Question 2Easier
Which of the following values of x satisfies the inequality 5x − 3 < 32?
Show answer and explanation
Answer: C
Subtract −3 from both sides: 5x < 35.
Divide by 5: x < 7.
Only 6 is less than 7. (x = 7 itself makes the two sides equal, so it doesn't work.)
- Question 3Easier
Which of the following values of x satisfies the inequality 6x + 1 < −35?
Show answer and explanation
Answer: C
Subtract 1 from both sides: 6x < −36.
Divide by 6: x < −6.
Only −10 is less than −6. (x = −6 itself makes the two sides equal, so it doesn't work.)
- Question 4Medium
Which of the following values of x satisfies the inequality −5x + 10 < −10?
Show answer and explanation
Answer: A
Subtract 10 from both sides: −5x < −20.
Divide by −5, and because it's negative, flip the inequality sign: x > 4.
Only 8 is greater than 4. (x = 4 itself makes the two sides equal, so it doesn't work.)
- Question 5Medium
Which of the following values of x satisfies the inequality −2x − 5 > −19?
Show answer and explanation
Answer: C
Subtract −5 from both sides: −2x > −14.
Divide by −2, and because it's negative, flip the inequality sign: x < 7.
Only 5 is less than 7. (x = 7 itself makes the two sides equal, so it doesn't work.)
- Question 6Medium
Which of the following values of x satisfies the inequality −3x + 7 < 7?
Show answer and explanation
Answer: D
Subtract 7 from both sides: −3x < 0.
Divide by −3, and because it's negative, flip the inequality sign: x > 0.
Only 1 is greater than 0. (x = 0 itself makes the two sides equal, so it doesn't work.)
- Question 7Easier
Which of the following values of x satisfies the inequality 2x + 8 > 2?
Show answer and explanation
Answer: B
Subtract 8 from both sides: 2x > −6.
Divide by 2: x > −3.
Only 1 is greater than −3. (x = −3 itself makes the two sides equal, so it doesn't work.)
- Question 8Easier
Which of the following values of x satisfies the inequality 2x − 5 > −9?
Show answer and explanation
Answer: D
Subtract −5 from both sides: 2x > −4.
Divide by 2: x > −2.
Only 2 is greater than −2. (x = −2 itself makes the two sides equal, so it doesn't work.)
- Question 9Easier
Which of the following values of x satisfies the inequality 3x + 6 > 27?
Show answer and explanation
Answer: B
Subtract 6 from both sides: 3x > 21.
Divide by 3: x > 7.
Only 11 is greater than 7. (x = 7 itself makes the two sides equal, so it doesn't work.)
- Question 10Easier
Which of the following values of x satisfies the inequality x + 9 < 11?
Show answer and explanation
Answer: D
Subtract 9 from both sides: x < 2.
Divide by 1: x < 2.
Only 1 is less than 2. (x = 2 itself makes the two sides equal, so it doesn't work.)
More Algebra practice
Questions people ask
Is this linear inequalities practice like the real SAT?
The questions follow the format of the digital SAT's Algebra domain: four answer choices built from common mistakes. They are written for this site; they are not official College Board questions.
How many practice questions are there?
As many as you want. Each math question is generated from a template with new numbers, and its answer is checked by code. Use "New set" for another ten.
Where is the domain on the test?
Algebra is one of the four content domains of the SAT Math section, alongside Advanced Math, Problem-Solving and Data Analysis, Geometry and Trigonometry.