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SAT Algebra: Linear Equations in One Variable — 16 MCQs with Solutions

Practice 16 original Digital SAT Math questions on linear equations in one variable. Each multiple-choice question includes four answer options, difficulty level, and a detailed worked solution. This independent educational resource is not affiliated with College Board.

SAT-001 | Easy

Solve 5x + 7 = 42.

  1. 5
  2. 6
  3. 7
  4. 8
Show correct answer and step-by-step solution

Correct answer: C. 7

  1. Subtract 7 from both sides: 5x = 35.
  2. Divide both sides by 5: x = 7.

SAT-002 | Easy

What is x if 3(x − 4) = 21?

  1. 3
  2. 7
  3. 9
  4. 11
Show correct answer and step-by-step solution

Correct answer: D. 11

  1. Divide by 3: x − 4 = 7.
  2. Add 4 to both sides: x = 11.

SAT-003 | Easy

Solve 2x − 9 = 15.

  1. 3
  2. 6
  3. 12
  4. 24
Show correct answer and step-by-step solution

Correct answer: C. 12

  1. Add 9 to both sides: 2x = 24.
  2. Divide by 2: x = 12.

SAT-004 | Easy

If x/4 + 3 = 8, what is x?

  1. 5
  2. 11
  3. 20
  4. 32
Show correct answer and step-by-step solution

Correct answer: C. 20

  1. Subtract 3: x/4 = 5.
  2. Multiply both sides by 4: x = 20.

SAT-005 | Easy

Solve 7 − 2x = −9.

  1. −8
  2. −1
  3. 1
  4. 8
Show correct answer and step-by-step solution

Correct answer: D. 8

  1. Subtract 7: −2x = −16.
  2. Divide by −2: x = 8.

SAT-006 | Medium

Solve 4(2x − 3) = 3x + 18.

  1. 3
  2. 5
  3. 6
  4. 10
Show correct answer and step-by-step solution

Correct answer: C. 6

  1. Expand: 8x − 12 = 3x + 18.
  2. Subtract 3x and add 12: 5x = 30.
  3. Divide by 5: x = 6.

SAT-007 | Medium

For what value of x is 5(x + 2) − 3(x − 4) = 30?

  1. 2
  2. 4
  3. 6
  4. 8
Show correct answer and step-by-step solution

Correct answer: B. 4

  1. Expand: 5x + 10 − 3x + 12 = 30.
  2. Combine like terms: 2x + 22 = 30.
  3. Subtract 22 and divide by 2: x = 4.

SAT-008 | Medium

Solve (x − 3)/5 = (x + 1)/7.

  1. −13
  2. 3
  3. 13
  4. 17
Show correct answer and step-by-step solution

Correct answer: C. 13

  1. Multiply both sides by 35: 7(x − 3) = 5(x + 1).
  2. Expand: 7x − 21 = 5x + 5.
  3. Subtract 5x, add 21, and divide by 2: x = 13.

SAT-009 | Easy

A streaming service charges a $12 fixed fee plus $4 per movie. If the total bill is $44, how many movies were rented?

  1. 6
  2. 7
  3. 8
  4. 11
Show correct answer and step-by-step solution

Correct answer: C. 8

  1. Let m be the number of movies: 12 + 4m = 44.
  2. Subtract 12: 4m = 32.
  3. Divide by 4: m = 8.

SAT-010 | Medium

Solve 0.3x + 1.2 = 4.8.

  1. 10
  2. 12
  3. 14
  4. 16
Show correct answer and step-by-step solution

Correct answer: B. 12

  1. Subtract 1.2: 0.3x = 3.6.
  2. Divide by 0.3: x = 12.

SAT-011 | Medium

The equation 9x − k = 4x + 15 has solution x = 6. What is k?

  1. 9
  2. 12
  3. 15
  4. 21
Show correct answer and step-by-step solution

Correct answer: C. 15

  1. Substitute x = 6: 54 − k = 24 + 15.
  2. Simplify: 54 − k = 39.
  3. Subtract 39 from 54: k = 15.

SAT-012 | Medium

Solve 2(x + 5) − (x − 7) = 22.

  1. 3
  2. 5
  3. 7
  4. 9
Show correct answer and step-by-step solution

Correct answer: B. 5

  1. Expand: 2x + 10 − x + 7 = 22.
  2. Combine like terms: x + 17 = 22.
  3. Subtract 17: x = 5.

SAT-013 | Hard

For which value of a does a(x − 2) = 3x + 6 have no solution for x?

  1. −3
  2. 0
  3. 3
  4. 6
Show correct answer and step-by-step solution

Correct answer: C. 3

  1. Expand: ax − 2a = 3x + 6.
  2. Rearrange: (a − 3)x = 2a + 6.
  3. For no solution, the coefficient of x must be zero while the constant is nonzero.
  4. Setting a = 3 gives 0x = 12, which is impossible.

SAT-014 | Hard

If 2(3x + p) = 6x + 14 is true for every real x, what is p?

  1. 3
  2. 5
  3. 7
  4. 14
Show correct answer and step-by-step solution

Correct answer: C. 7

  1. Expand: 6x + 2p = 6x + 14.
  2. Subtract 6x: 2p = 14.
  3. Divide by 2: p = 7.

SAT-015 | Medium

A tank initially contains 18 liters. Water flows in at 2.5 liters per minute. After how many minutes will it hold 60 liters?

  1. 14.8
  2. 16.8
  3. 18.2
  4. 31.2
Show correct answer and step-by-step solution

Correct answer: B. 16.8

  1. Let t denote the number of minutes. Then 18 + 2.5t = 60.
  2. Subtract 18: 2.5t = 42.
  3. Divide by 2.5: t = 16.8 minutes.

SAT-016 | Hard

If (2x − 5)/3 − (x + 1)/2 = 1, what is x?

  1. 11
  2. 17
  3. 19
  4. 23
Show correct answer and step-by-step solution

Correct answer: C. 19

  1. Multiply each term by 6: 2(2x − 5) − 3(x + 1) = 6.
  2. Expand: 4x − 10 − 3x − 3 = 6.
  3. Combine: x − 13 = 6.
  4. Add 13: x = 19.

Continue SAT Mathematics Preparation

After completing these 16 linear-equation questions, return to the Digital SAT Mathematics study guide for other topics. You can also browse all subjects on EduConceptHub.

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