One-variable linear equations drills

Solve one-step and two-step linear equations in one variable.

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

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How to solve one-step and two-step equations

Get \(x\) alone by undoing each operation. Do the same thing to both sides.

  1. Undo adding or subtracting first.
  2. Then undo multiplying by dividing.
  3. Check: put your answer back into the original equation.

Example: \(7x + 6 = -8\). Subtract \(6\) from both sides: \(7x = -14\). Divide both sides by \(7\): \(x = -2\). Check: \(7(-2) + 6 = -8\).

Common traps:

Worked examples

Example 1.
Solve for \(x\): \(x - 3 = -17\).
Show answer and explanation
Answer:
C

Isolate \(x\) by adding 3 to both sides: \(x = -17 + 3 = -14\). (Subtracting \(3\) instead gives \(-20\). Subtracting in the wrong order, \(-3 - (-17)\), gives \(14\). Answering with the right side, \(-17\), skips the step that removes the \(- 3\).)

Example 2.
Solve for \(x\): \(-7x = -35\).
Show answer and explanation
Answer:
C

Divide both sides by -7: \(x = -35 \div (-7) = 5\). (Dividing the other way, \(-7 \div (-35)\), gives \(1/5\). Losing the sign of the answer gives \(-5\). Treating \(-7x\) as \(x - 7\) gives \(-28\).)

Example 3.
Solve for \(x\): \(-2x + 7 = 25\).
Show answer and explanation
Answer:
A

Subtract 7 from both sides: \(-2x = 25 - 7 = 18\). Divide by -2: \(x = 18 \div (-2) = -9\). (Adding \(7\) instead gives \(-16\). Dividing by -2 first and then subtracting 7 gives \(-39/2\). Stopping before the division gives \(18\).)