 # 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 4x = 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 4x = 24

Solution:

4x = 24 (Divide by 4 on both sides)

x = 6

Check:

4x = 24

4 • 6 = 24 (Substitute x = 6 into original equation)

Example of solving equations using division.
Example:
2x = -140

### 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)

Example of solving equations by multiplication.
Example:
x/9 = -6

### 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: Example of solving equations by taking the reciprocal.
Example:
2/3 x = -4/3

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