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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