Solve Two-Step Equations

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What is a two-step equation?

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A two-step equation is an algebraic equation that requires two operations to solve for the variable. It typically involves isolating the variable on one side of the equation.

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How do you isolate a variable in a two-step equation?

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To isolate a variable in a two-step equation, perform the inverse operations in the reverse order of operations: first, eliminate any addition or subtraction, then eliminate any multiplication or division.

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What is the first step to solve the equation 8/11(n - 10) = 64?

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The first step is to multiply both sides of the equation by the reciprocal of 8/11, which is 11/8, to eliminate the fraction.

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What does it mean to perform the inverse operation?

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Performing the inverse operation means applying the opposite mathematical operation to cancel out a term. For example, the inverse of addition is subtraction, and the inverse of multiplication is division.

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How do you solve the equation 0.25(3 + a) = 0.5?

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First, divide both sides by 0.25 to isolate the term (3 + a), then subtract 3 from both sides to solve for a.

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What is the solution to the equation -7(z - 6) = -70?

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The solution is z = 16. First, divide both sides by -7, then add 6 to both sides.

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What is the significance of the distributive property in solving equations?

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The distributive property allows you to multiply a single term by each term inside a parenthesis, which is essential for simplifying equations before solving.

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How do you handle negative coefficients in equations?

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When dealing with negative coefficients, apply the same principles of inverse operations. For example, if you have -7(z - 6) = -70, divide both sides by -7 to simplify.

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What is the solution to the equation 5/9(8 + c) = -20?

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The solution is c = -44. First, multiply both sides by 9/5 to eliminate the fraction, then solve for c.

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What is the process to solve (t + 9)20 = 140?

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First, divide both sides by 20 to isolate (t + 9), then subtract 9 from both sides to find t.