Algebra · Math

Linear equations in one variable

Solving linear equations in one variable, including equations with variables on both sides, and questions about how many solutions an equation has.

26 questions in the bank · 9 easier · 8 medium · 9 harder · this domain is ≈35% of the section

Learn it in the Guide

What to watch for

For solution counts: if the variable cancels and leaves a true statement, there are infinitely many solutions; if it leaves a false one, there are none. A linear equation never has exactly two.

How the question is worded

These are the actual stems used in the bank — the SAT reuses a small set of wordings, and recognising them saves time on test day.

  • What value of x is the solution to the equation 3x − 6 = −2x + 4?
  • What value of x is the solution to the equation 4x + 4 = 2x − 4?
  • What value of x is the solution to the equation 8x = 6x + 4?
  • What value of x is the solution to the equation 2x − 2 = 6x + 3?

Worked examples

easyWhat value of x is the solution to the equation 3x − 6 = −2x + 4?

What value of x is the solution to the equation 3x − 6 = −2x + 4?

  • A. −2
  • B. 2
  • C. 3
  • D. 10

Answer: B. 2

Explanation

Collect the x-terms on one side and constants on the other: 3x − 6 = −2x + 4 gives 5x = 10, so x = 2. Substituting back confirms both sides are equal.

mediumWhat value of x is the solution to the equation 4x + 4 = 2x − 4?

What value of x is the solution to the equation 4x + 4 = 2x − 4?

  • A. −4/3
  • B. −4
  • C. 4
  • D. −3

Answer: B. −4

Explanation

Collect the x-terms on one side and constants on the other: 4x + 4 = 2x − 4 gives 2x = −8, so x = −4. Substituting back confirms both sides are equal.

hardHow many solutions does the equation 6x + 6 = 3(4x + 8) have?

How many solutions does the equation 6x + 6 = 3(4x + 8) have?

  • A. It cannot be determined
  • B. Infinitely many
  • C. Exactly one
  • D. Zero

Answer: C. Exactly one

Explanation

Distribute: 3(4x + 8) = 12x + 24. The x-coefficients (6 and 12) are different, so the x-terms do not cancel and the equation solves to a single value of x. Different slopes cross exactly once.