How do I solve an equation with the unknown on both sides, like 5x − 3 = 2x + 9?

The plan is to collect all the x terms on one side and all the plain numbers on the other. Start with 5x − 3 = 2x + 9. Move the 2x from the right to the left; when it crosses the equals sign it changes sign to −2x, giving 5x − 2x − 3 = 9, which is 3x − 3 = 9. Now move the −3 to the right where it becomes +3: 3x = 9 + 3 = 12. Finally divide both sides by 3: x = 12 ÷ 3 = 4. Always check by substituting back: left side 5 × 4 − 3 = 17, right side 2 × 4 + 9 = 17. Both sides equal 17, so x = 4 is correct.