Multi-step equations drills

Solve multi-step equations, including variables on both sides.

Free, timed SHSAT practice sets on multi-step equations— every question includes a full worked explanation, and there's no account required.

Loading questions…

How to solve multi-step equations

Work in this order:

  1. Distribute to remove parentheses. Multiply every term inside.
  2. Move the \(x\)-terms to one side and the numbers to the other. Add or subtract the same term on both sides.
  3. Divide by the number in front of \(x\).
  4. Check your answer in the original equation.

Example: \(6(x - 6) = -2x + 12\). Distribute: \(6x - 36 = -2x + 12\). Add \(2x\) to both sides: \(8x - 36 = 12\). Add \(36\): \(8x = 48\). Divide: \(x = 6\). Check: \(6(0) = 0\) and \(-12 + 12 = 0\).

Common traps:

Worked examples

Example 1.
Solve for \(x\): \(5x - 10 = -2x + 4\).
Show answer and explanation
Answer:
A

Move the \(x\)-terms to one side and the numbers to the other: \(7x = 4 - (-10) = 14\). Divide: \(x = 14 \div 7 = 2\). (Adding the \(x\)-terms, \(3x\), instead of subtracting them gives \(14/3\). Subtracting the numbers in the wrong order, \(-10 - 4\), gives \(-2\). Stopping before the division gives \(14\).)

Example 2.
Solve for \(x\): \(-2(x - 8) = 12\).
Show answer and explanation
Answer:
B

Distribute: \(-2(x - 8) = -2x + 16 = 12\). Subtract 16 from both sides: \(-2x = -4\). Divide by -2: \(x = 2\). (Multiplying only the \(x\) by \(-2\) gives \(-2x - 8 = 12\) and \(-10\). Dividing by -2 first and then subtracting \(8\) gives \(-14\). Stopping before the division gives \(-4\).)

Example 3.
Solve for \(x\): \(-7(x - 1) = 6x - 58\).
Show answer and explanation
Answer:
C

Distribute: \(-7x + 7 = 6x - 58\). Move \(x\)-terms together: \(-13x = -65\). Divide: \(x = 5\). (Multiplying only the \(x\) by \(-7\) gives \(57/13\). Moving \(+ 7\) across without changing its sign gives \(51/13\). Adding the \(x\)-terms, \(-x\), instead of subtracting them gives \(65\).)