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Solving Equations by Division, Multiplication or taking the Reciprocal



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More Lessons for Algebra

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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)

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.



 

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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