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Solving Equations using Addition and Subtraction

Learn how to solve equations by isolating the variable using addition and subtraction. Practice with examples and check your answers.

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Solving Equations using Addition and Subtraction

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  1. Section 3.1 Solving Equations Using Addition and Subtraction.

  2. To Solve an Equation means... To isolate the variable having a coefficient of 1 on one side of the equation. Ex: x = 5 is solved for x. y = 2x - 1 is solved for y.

  3. r + 16 = -7 Here is an example…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!

  4. 1) Solve r + 16 = -7 To solve, you must get the variable by itself!! What is the variable? 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

  5. 1) Solve r + 16 = -7 - 16 -16 r = -23 -23 + 16 = -7 • Draw a line 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

  6. 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

  7. 2) Solve x + 2 = -3 - 2 - 2 x = -5 -5 + 2 = -3 • Draw a line 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!

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

  9. 3) Solve 8 = m - 3 + 3 + 3 11= m 8 = 11 - 3 • Draw a line 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

  10. REMEMBER: When solving equations, we want to eliminate double signs. Example 1 y + (-3) = 8 is rewritten as y – 3 = 8 p – (-5) = 6 is rewritten as p + 5 = 6 Example 2 As a general rule, replace “+ (- )” with “–” and “– (- )” with “+”. This will make things less confusing in the future!

  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 • Add 3 to both sides • Simplify vertically • Check your answer by substituting your answer back into the problem

  12. 5) Solve. x - (-2) = 1 • Draw a line 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

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

  14. Homework: 9/9/13 Workbook page 13 Solving Equations by Adding or Subtracting

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