Transforming Equations
3-2Transforming Equations: Multiplication and Division
Overview
Multiply or divide both sides by the same nonzero number to isolate the variable.
Key ideas
- Divide both sides by the variable’s coefficient.
- To clear a fraction, multiply by the reciprocal.
- Never divide by zero.
Worked examples
Example 1
Problem. Solve 4x = 28.
Solution. Divide by 4: x = 7.
Example 2
Problem. Solve x/3 = −5.
Solution. Multiply by 3: x = −15.
Practice
Try each one. Click Show answer when ready.
- 1.
Solve 6y = −42.
- 2.
Solve x/5 = 4.
- 3.
Solve (2/3)x = 8.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Solve: −4x = 28.
- 2.
Solve: x/−5 = −3.