Solve linear equations in one unknown with the unknown on both sides

Follow this one with me, a step at a time. Try to guess each step first.

Worked example 1

Solve: 2x + 4 = −2x + 20

Remember: Collect the terms in x on one side and the numbers on the other. A term changes sign when it crosses the equals sign.

Move the terms: 2x + 2x = 20 − 4.
Collect them: 4x = 16.
Divide both sides by 4: x = 4.
Check: both sides equal 12 when x = 4.

Common mistakes

The method looks right and the arithmetic is out by one. Substitute your answer to check.
The size of the solution is right and its sign is not. Substitute it into both sides to check.
Moved a number across the equals sign without changing its sign.