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Solving Equations with Addition and Subtraction: A Comprehensive Guide

This guide teaches students how to solve equations using addition and subtraction. It illustrates the concept of maintaining balance in equations by applying the same operation to both sides and emphasizes the importance of isolating the variable. Step-by-step examples include solving problems like r + 16 = -7 and x + 2 = -3, demonstrating how to draw "the river" to separate the equation. The guide also covers eliminating double signs and checking answers. Perfect for homework and test preparation!

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Solving Equations with Addition and Subtraction: A Comprehensive Guide

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  1. ObjectiveThe student will be able to: solve equations using addition and subtraction. Designed by Skip Tyler, Varina High School

  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 “the river” to separate the equation into 2 sides • Subtract 16 from both sides • Simplify vertically • Check your answer by substituting your answer back into the problem

  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 “the river” to separate the equation into 2 sides • Subtract 2 from both sides • Simplify vertically • Check your answer by substituting your answer back into the problem 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 “the river” to separate the equation into 2 sides • Add 3 to both sides • Simplify vertically • Check your answer by substituting your answer back into the problem

  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. 4) Solve y + (-3) = 7 y – 3 = 7 + 3 +3 y = 10 10 + (-3) = 7 • Draw “the river” to separate the equation into 2 sides • Eliminate the double sign • Add 3 to both sides • Simplify vertically • Check your answer by substituting your answer back into the problem

  11. Draw “the river” to separate the equation into 2 sides • Eliminate the double sign • 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

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

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