# Solving Equations by Division, Multiplication or taking the Reciprocal

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In this lesson, we will look at solving equations by division, multiplication or taking the reciprocal.

** Solving Equations by Division **

Consider the equation 4*x* = 24. The variable is being multiplied by 4. To write an equivalent equation with the variable isolated, divide by 4 on both sides.

* Example: *

Solve 4*x* = 24

* Solution: *

4*x* = 24

(Divide by 4 on both sides)

* x* = 6

** Check: **

4*x* = 24

4 • 6 = 24

(Substitute *x* = 6 into original equation)
The following video shows another example of solving equations using division.

** Solving Equations by Multiplication **

To solve the equation , we notice that the variable is being divided by 5. To write an equivalent equation with the variable isolated, multiply by 5 on both sides.

* Example: *

Solve

* Solution: *

* Check: *

(Substitute *x* = 30 in the original equation)

The following video gives another example of solving equations by multiplication.

### Solving equations by taking the reciprocal

Consider the equation . The variable is being multiplied by . To write an equivalent equation with the variable isolated, multiply by the reciprocal, which is , on both sides.

* Example: *

Solve

* Solution: *

* Check: *

The following video shows another example of solving equations by taking the reciprocal.

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