2-Step Equations using Distributive Property

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What is a 2-step equation?

Back

A 2-step equation is an algebraic equation that requires two operations to isolate the variable. It typically involves addition or subtraction followed by multiplication or division.

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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 two or more terms inside a set of parentheses.

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How do you solve the equation 2(x - 7) = 10?

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First, apply the distributive property: 2x - 14 = 10. Then, add 14 to both sides: 2x = 24. Finally, divide by 2: x = 12.

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What is the first step in solving the equation -5(20 + 2x) = 400?

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Apply the distributive property: -100 - 10x = 400. Then, add 100 to both sides: -10x = 500.

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What is the solution to the equation -3(4b + 7)?

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Distributing gives -12b - 21. This expression is not an equation, so it cannot be solved for a specific value.

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How do you solve the equation (2/3)(n + 6) = 10?

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Multiply both sides by the reciprocal of 2/3, which is 3/2: n + 6 = 15. Then, subtract 6 from both sides: n = 9.

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

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

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How do you combine like terms in an equation?

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Combine like terms by adding or subtracting coefficients of the same variable or constant terms.

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What is the solution to the equation -2d - 5 - 2d = -9?

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Combine like terms: -4d - 5 = -9. Add 5 to both sides: -4d = -4. Divide by -4: d = 1.

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What is the importance of checking your solution in an equation?

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Checking your solution ensures that the value satisfies the original equation, confirming that the solution is correct.