Solving Problems
3-5Equations with the Variable on Both Sides
Overview
Move all variable terms to one side and constants to the other, then solve.
Key ideas
- Subtract the smaller variable term from both sides.
- Then isolate the variable with usual moves.
- Some equations have no solution or all real numbers as solutions.
Worked examples
Example 1
Problem. Solve 5x − 3 = 2x + 9.
Solution. Subtract 2x: 3x − 3 = 9. Add 3: 3x = 12. Divide: x = 4.
Practice
Try each one. Click Show answer when ready.
- 1.
Solve 7x + 2 = 3x + 14.
- 2.
Solve 4(x − 1) = 2x + 6.
- 3.
Solve 6 − 2x = 5x − 8.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Solve: 5x − 3 = 2x + 9.
- 2.
Solve: 7 − 2y = 3y − 8.