In this lesson, we will look at examples of how to solve and check an equations involving the distributive property.

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#### Remember — Distributive Property

tells us that we can remove the parentheses by distributing (by multiplying) the number in front of parentheses to each term inside the parentheses.

For example one way to write the formula for finding

the perimeter of a rectangle is: $\color{purple}{P=2(l+w)}$

or we could distribute the 2 and get: $\color{purple}{P=2l+2x}$

#### Try these two problems:

1. Dan had 61 ft fencing that he wants to use to surround his garden. If the width is x ft. and the length is 1.5x+8 ft. what are the dimensions of his garden?

2. $5x-3(2x-4)=21$

#### Solutions:

1. Original problem: Dan had $61$ ft fencing that he wants to use to surround his garden. If the width is $x$ ft. and the length is $1.5x+8$ ft. what are the dimensions of his garden?

2. Original problem |
$ 5x \color{red}{-}3(2x\color{red}{-} 4)=21$ |

a. Change all the subtraction problems to adding the opposite: |
$5x \color{blue}{+{^-3}}(2x\color{blue}{+{^-4}})=21$ |

b. Remove the parentheses by distributing the $^-3$ |
$5x +\color{#ff1493}{{^-6x}+12}=21$ |

c. Combine like terms: |
$\color{green}{^-1x}+12=21$ |

d. Solve for $x$ |
${^-1x}+12\color{purple}{-12}=21\color{purple}{-12}$ |

${^-1x}=9$ | |

$\color{red}{x={^-9}}$ |