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SECTION 3.1 Solving Equations Using Addition and Subtraction.

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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.

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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!

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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

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- 16 -16 r = -23 -23 + 16 = -7 1) SOLVE R + 16 = -7 1. Draw a line to separate the equation into 2 sides 2. Subtract 16 from both sides 3. Simplify vertically 4. Check your answer by substituting your answer back into the problem

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2) SOLVE X + 2 = -3 GET THE VARIABLE BY ITSELF. WHAT IS YOUR FIRST STEP? 1. Add 2 to both sides 2. Subtract 2 from both sides 3. Add 3 to both sides 4. Subtract 3 from both sides Answer Now

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2) SOLVE X + 2 = -3 1. Draw a line to separate the equation into 2 sides 2. Subtract 2 from both sides 3. Simplify vertically 4. Check your answer by substituting your answer back into the problem - 2 - 2 x = -5 -5 + 2 = -3 On homework and tests, be sure to check your work!! There is no reason why you should miss a problem!

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3) SOLVE 8 = M - 3 1. m = 5 2. m = 11 3. m = 24 4. m = 8/3 Answer Now

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3) SOLVE 8 = M - 3 + 3+ 3 11= m 8 = 11 - 3 1.Draw a line to separate the equation into 2 sides 2.Add 3 to both sides 3.Simplify vertically 4.Check your answer by substituting your answer back into the problem

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REMEMBER: 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! Example 1 Example 2

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4) SOLVE Y + (-3) = 7 y – 3 = 7 + 3 +3 y = 10 10 + (-3) = 7 1.Draw a line to separate the equation into 2 sides 2.Eliminate the double sign 3.Add 3 to both sides 4.Simplify vertically 5.Check your answer by substituting your answer back into the problem

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5) SOLVE. X - (-2) = 1 x + 2 = 1 - 2 - 2 x = -1 (-1) + 2 = 1 1.Draw a line to separate the equation into 2 sides 2.Eliminate the double sign 3.Subtract 2 from both sides 4.Simplify vertically 5.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? 6.Check your answer

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SOLVE Y – (-3) = 7 1. y = 10 2. y = 4 3. y = -10 4. y = -4 Answer Now

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HOMEWORK: 9/9/13 Workbook page 13 Solving Equations by Adding or Subtracting

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