Sometimes our variable is being multiplied to a number, in this case, we use the multiplicative inverse (which we learned about in our lessons on fractions) to isolate our variable. In all cases when we’re solving for variables, it is important to remember that anything we do to one side of the equation, we must do to the other.

This video uses the word isolate.

Solving for a Variable on One Side Part 2-Multiplication

Video Source (05:08 mins) | Transcript

As shown in the video, to isolate a variable when it’s being multiplied, we multiply both sides of the equation with the multiplicative inverse of the number. Remember, the multiplicative inverse is the opposite fraction (example: \(3\) and \( {\dfrac {1}{3}} \) ).

## Additional Resources

- Khan Academy: Inverse Property of Multiplication (03:16 mins, Transcript)
- Khan Academy: One-step Division Equations (11:05 mins, Transcript)
- Khan Academy: One-step Multiplication Equations (02:22 mins, Transcript)

### Practice Problems

**Solve for the variable:**

- \(7{\text{L}} = 14\) (Solution
- \(5{\text{Z}} = 20\) (Solution
- \(5{\text{H}} = 25\) (Solution
- \(4{\text{U}} = -24\) (Solution
- \(7{\text{W}} = 63\) (Video Solution
- \(-2{\text{b}} = 16\) (Video Solution

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