The rules that solve most questions
- Do the same operation to both sides. Subtract the smaller x term from both sides first so the coefficient stays positive.
- Distribute before you collect terms: 3(x − 2) is 3x − 6, not 3x − 2.
- When the equation has fractions, multiply every term by the common denominator to clear them.
- Check by substituting your answer into both sides. On a timed test, this takes ten seconds and catches sign errors.
Traps the wrong answers are built on
- Adding a term to one side instead of subtracting it from both (a sign error).
- Dividing by the wrong coefficient after collecting terms.
- Answering −x when the question asks for x.
Worked example
If 7x + 10 = −2x + 64, what is the value of x?
- A. −6
- B. 5
- C. 7
- D. 6
Answer: D. Collect the x terms on one side: 7x − (−2x) = 64 − 10. That gives 9x = 54. Divide both sides by 9: x = 6. Check: 7(6) + 10 = 52 and −2(6) + 64 = 52. Both sides match.
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
If 7x + 10 = −2x + 64, what is the value of x?
Show answer and explanation
Answer: D
Collect the x terms on one side: 7x − (−2x) = 64 − 10.
That gives 9x = 54.
Divide both sides by 9: x = 6.
Check: 7(6) + 10 = 52 and −2(6) + 64 = 52. Both sides match.
- Question 2Easier
If 9x + 6 = −2x + 116, what is the value of x?
Show answer and explanation
Answer: D
Collect the x terms on one side: 9x − (−2x) = 116 − 6.
That gives 11x = 110.
Divide both sides by 11: x = 10.
Check: 9(10) + 6 = 96 and −2(10) + 116 = 96. Both sides match.
- Question 3Easier
If 3x + 2 = x + 24, what is the value of x?
Show answer and explanation
Answer: A
Collect the x terms on one side: 3x − x = 24 − 2.
That gives 2x = 22.
Divide both sides by 2: x = 11.
Check: 3(11) + 2 = 35 and (11) + 24 = 35. Both sides match.
- Question 4Easier
If 7x + 15 = 6x + 7, what is the value of x?
Show answer and explanation
Answer: A
Collect the x terms on one side: 7x − 6x = 7 − 15.
That gives x = −8.
Divide both sides by 1: x = −8.
Check: 7(−8) + 15 = −41 and 6(−8) + 7 = −41. Both sides match.
- Question 5Easier
If 9x − 9 = −3x − 33, what is the value of x?
Show answer and explanation
Answer: C
Collect the x terms on one side: 9x − (−3x) = −33 − (−9).
That gives 12x = −24.
Divide both sides by 12: x = −2.
Check: 9(−2) − 9 = −27 and −3(−2) − 33 = −27. Both sides match.
- Question 6Easier
If 4x + 9 = −3x + 23, what is the value of x?
Show answer and explanation
Answer: D
Collect the x terms on one side: 4x − (−3x) = 23 − 9.
That gives 7x = 14.
Divide both sides by 7: x = 2.
Check: 4(2) + 9 = 17 and −3(2) + 23 = 17. Both sides match.
- Question 7Easier
If 4x − 5 = 5x − 10, what is the value of x?
Show answer and explanation
Answer: C
Collect the x terms on one side: 4x − 5x = −10 − (−5).
That gives −x = −5.
Divide both sides by −1: x = 5.
Check: 4(5) − 5 = 15 and 5(5) − 10 = 15. Both sides match.
- Question 8Easier
If 4x − 7 = −3x + 21, what is the value of x?
Show answer and explanation
Answer: B
Collect the x terms on one side: 4x − (−3x) = 21 − (−7).
That gives 7x = 28.
Divide both sides by 7: x = 4.
Check: 4(4) − 7 = 9 and −3(4) + 21 = 9. Both sides match.
- Question 9Easier
If 9x − 10 = 4x + 25, what is the value of x?
Show answer and explanation
Answer: C
Collect the x terms on one side: 9x − 4x = 25 − (−10).
That gives 5x = 35.
Divide both sides by 5: x = 7.
Check: 9(7) − 10 = 53 and 4(7) + 25 = 53. Both sides match.
- Question 10Easier
If 6x + 14 = x + 19, what is the value of x?
Show answer and explanation
Answer: C
Collect the x terms on one side: 6x − x = 19 − 14.
That gives 5x = 5.
Divide both sides by 5: x = 1.
Check: 6(1) + 14 = 20 and (1) + 19 = 20. Both sides match.
More Algebra practice
Questions people ask
Is this linear equations in one variable 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.