Solve Equations Using the Distributive Property

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What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a set of parentheses.

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What are coefficients in an expression?

Back

Coefficients are the numerical factors in terms of an algebraic expression. For example, in 8y + 5 - 35p, the coefficients are 8 and -35.

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How do you solve the equation -3(f - 8) = 39?

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First, distribute -3 to both terms inside the parentheses: -3f + 24 = 39. Then, isolate f to find the solution.

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What is the first step to solve 4(x + 2) = -16?

Back

The first step is to distribute 4 to both x and 2, resulting in 4x + 8 = -16.

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How do you express the total cost of selling 9 apples at $0.75 each and 9 pears at $0.60 each?

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The expression is 9($0.75 + $0.60).

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What is an equivalent equation for \( \frac{1}{3}(6x + 15) = 7 \)?

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An equivalent equation is \( 2x + 5 = 7 \).

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What does it mean to isolate a variable in an equation?

Back

Isolating a variable means to manipulate the equation so that the variable is on one side and all other terms are on the opposite side.

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What is the result of applying the Distributive Property to 5(x + 3)?

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The result is 5x + 15.

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How do you combine like terms in the expression 3x + 4x - 2?

Back

Combine like terms to get 7x - 2.

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What is the solution to the equation 2(x - 4) = 10?

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First, distribute: 2x - 8 = 10. Then, add 8 to both sides: 2x = 18. Finally, divide by 2: x = 9.