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Solving Equations Using Addition and Subtraction: A Step-by-Step Guide

This educational resource provides a comprehensive guide for students to master solving equations using addition and subtraction. With clear examples, such as r + 16 = -7 and x + 2 = -3, learners are introduced to the concept of inverse operations to isolate variables. The document emphasizes the importance of maintaining balance in equations and includes strategies for checking answers through substitution. Ideal for homework and test preparation, this guide ensures students gain the confidence needed to tackle similar problems effectively.

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Solving Equations Using Addition and Subtraction: A Step-by-Step Guide

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  1. ObjectiveThe student will be able to: solve equations using addition and subtraction. Designed by Skip Tyler, Edited by Mr. Nealey

  2. r + 16 = -7 1) Solve r + 16 = -7 Think of this equation as a balance scale. Whatever you do to one side has to be done to the other to keep it balanced!

  3. 1) Solve r + 16 = -7 To solve, you must get the variable by itself. What number is on the same side as r? 16 To get r by itself, we must undo the “add 16”. What is the opposite of addition? Subtract 16

  4. 1) Solve r + 16 = -7 - 16 -16 r = -23 -23 + 16 = -7 • Draw a line to separate the equation into 2 sides • Inverse Operations: Subtract 16 from both sides • Simplify vertically • Check your answer by substituting your answer back into the original equation.

  5. Answer Now 2) Solve x + 2 = -3Get the variable by itself. What is your first step? • Add 2 to both sides • Subtract 2 from both sides • Add 3 to both sides • Subtract 3 from both sides

  6. 2) Solve x + 2 = -3 - 2 - 2 x = -5 -5 + 2 = -3 • Draw a line to separate the equation into 2 sides • Inverse Operations: Subtract 2 from both sides • Simplify vertically • Check your answer by substituting your answer back into the original equation. On homework and tests, be sure to check your work!! There is no reason why you should miss a problem!

  7. Answer Now 3) Solve 8 = m - 3 • m = 5 • m = 11 • m = 24 • m = 8/3

  8. 3) Solve 8 = m - 3 + 3 + 3 11= m 8 = 11 - 3 • Draw a line to separate the equation into 2 sides • Inverse Operations: Add 3 to both sides • Simplify vertically • Check your answer by substituting your answer back into the original equation.

  9. When solving equations, we want to eliminate double signs. y + (-3) = 8 is rewritten as y – 3 = 8 p – (-5) = 6 is rewritten as p + 5 = 6 As a general rule, replace “+ (- )” with “–”and “– (- )” with “+”. This will make things less confusing in the future!

  10. As a general rule, • replace “+ (- )” with “–” • replace “– (- )” with “+”. • This will make things less confusing in the future when you are solving the equation!

  11. 4) Solve y + (-3) = 7 y – 3 = 7 + 3 +3 y = 10 10 + (-3) = 7 • Draw a line to separate the equation into 2 sides • Eliminate the double sign • Inverse Operations: Add 3 to both sides • Simplify vertically • Check your answer by substituting your answer back into the original equation

  12. Draw a line to separate the equation into 2 sides • Eliminate the double sign • Inverse Operations: Subtract 2 from both sides • Simplify vertically • We haven’t gotten x by itself. If we read this aloud, it is “the opposite of x equals -1”. What would x be equal? • Check your answer -x + 2 = 1 - 2 - 2 -x = -1 x = 1 -(1) + 2 = 1 5) Solve. -x - (-2) = 1

  13. Answer Now Solve -y – (-3) = 7 • y = 10 • y = 4 • y = -10 • y = -4

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