Equations with the Distributive Property

Warm Up

Use the distributive property to solve equations by distributing a

factor to all terms within parenthesis, then solve for the

variable.

It is necessary to apply the distributive property before

isolating the variable on one side because the order of operations

states that expressions in parenthesis are simplified first.

Remember, only the terms within the parenthesis are multiplied by

the factor outside of the perenthesis.

Fractions can be eliminated before applying the distributive property

to allow for distributing with whole numbers, which are easier to work

with.

2(x - 6) + 3 = 4 + x

3x - 8 = 10 - 3(x - 4)

The Distributive Property can help you solve equations when an

equation contains an expression in parentheses multiplied by a factor,

the Distributive Property allows you to distribute the factor and get rid of the parentheses. This allows

the equation to be solved.

Each year Chana uses her income from her job to pay for 80% of her college tuition. Next year Chana

will need to contribute $2,000 toward her tuition. Next year the tuition will be $600 more than this

year’s tuition. How much is this year’s tuition?

As part of a school contest, Sarah and Luis are playing a math game. Sarah

must pick a number between 1 and 50 and give Luis clues so he can write an equation to find her number. Sarah

says, “If I subtract 5 from my number, multiply that quantity by 4, and then add 7 to the result, I get 35.” What equation can Luis write based on Sarah’s clues and what is Sarah’s

number?

Explain how to solve

5[3(x + 4) - 2(1 - x)] - x - 15 = 14x + 45.

Then solve the equation.

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