Most linear-equation errors are procedural, not conceptual. Use the same sequence every time: simplify, isolate the variable term, divide, then verify.

Example 1: one variable

Solve 3x + 7 = 28.

  1. Subtract 7 from both sides: 3x = 21.
  2. Divide both sides by 3: x = 7.
  3. Check: 3(7)+7=28.

Example 2: variables on both sides

Solve 5x - 4 = 2x + 17.

  1. Subtract 2x: 3x-4=17.
  2. Add 4: 3x=21.
  3. Divide by 3: x=7.

The highest-value check

Substitute your answer into the original equation—not a simplified line. This catches a copied sign or dropped constant immediately.

Common trap: an operation must affect both complete sides. Writing 3x+7-7=28 changes only one side and breaks equality.