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What Is Solving and Explaining Two-Step Equations Involving Whole Numbers and Using Inverse Operations? • An algebraic equation is an expression in which a letter represents an unknown number such as, n + 5 = 11 (n = 6). • An inverse operation is one that “undoes” or reverses another. Addition and subtraction are inverse operations, and so are multiplication and division. • Using an inverse operation allows us to calculate the value of the unknown number by moving all the known numbers to one side of the equation. • Two-step equations involve balancing both sides of the equation. To solve 5 + n = 11, subtract 5 (the inverse operation of addition) from both sides: n = 11 – 5. Perform the operation and n = 6 How to solve two-step equations involving whole numbers by using inverse operations: • To solve a two-step equation, the unknown number must be by itself on one side of the equation. This happens by performing inverse operations. • An algebraic equation must stay in balance, so whatever is done to one side must be done to the other. To solve this problem: n – 6 = 4 Add 6 to both sides of the equation because addition is the inverse of subtraction n = 10. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

• Just as addition and subtraction are inverse operations, so are multiplication and division. To solve this problem: 6n = 30 Divide both sides of the equation by 6 because division is the inverse of multiplication n = 5. • When solving two-step equations, first add or subtract both sides using the inverse operation of the one in the equation. Addition and subtraction are ALWAYS done first. 2n + 4 = 14 First subtract 4 from each side 2n = 10 Then divide each side by 2 n = 5 • Here are some two-step equations. Notice how the addition or subtraction is done first to balance the equation. The inverse operation is used to clear the addition or subtraction. Then an inverse operation is used to solve the problem n/8 – 6 = 10 (add 6 to both sides) n/8 = 16 (multiply both sides by 8) n = 128 5n + 5 = 20 (subtract 5 from both sides) 5n = 15 (divide both sides by 5) n = 3 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Try This! 12n – 5 = 31 ______________________________________________ n/7 + 5 = 31 ______________________________________________ 9n + 4 = 40 ______________________________________________ n/6 – 18 = 2 ______________________________________________ 3n – 14 = 16 ______________________________________________ © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.