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Equations with the Distributive Property

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Warm Up

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Use the distributive property to solve equations by distributing a factor to all terms within parenthesis, then solve for the variable.

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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.

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Remember, only the terms within the parenthesis are multiplied by the factor outside of the perenthesis.

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Fractions can be eliminated before applying the distributive property to allow for distributing with whole numbers, which are easier to work with.

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2(x - 6) + 3 = 4 + x 3x - 8 = (x - 4)

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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.

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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?

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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?

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Explain how to solve 5[3(x + 4) - 2(1 - x)] - x - 15 = 14x Then solve the equation.

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