Solving Equations by Adding or Subtracting

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Solving Equations by Adding or Subtracting

• Objective Solve equations using the addition and
  subtraction properties of equalities.

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Subtraction Property of Equality
For any numbers a, b, and c, if a b, then a c b c.
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Example 1 Solve x 9 5. Check your solution.
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Example 1 Solve x 9 5. Check your
solution. x 9 5 -9 -9 Subtract 9
from each side
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Example 1 Solve x 9 5. Check your
solution. x 9 5 9 - 9 Subtract
9 from each side. x -4 Check x 9 5
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Example 1 Solve x 9 5. Check your
solution. x 9 5 9 - 9 Subtract
9 from each side. x -4 Check x 9 5
-4 9 ? 5 Replace x with -4.
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Example 1 Solve x 9 5. Check your
solution. x 9 5 9 - 9 Subtract
9 from each side. x -4 Check x 9 5
-4 9 ? 5 Replace x with -4.
5 5 The solution is x -4.
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Addition Property of Equality
For any numbers a, b, and c, if a b, then a c b c.
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Example 2 Solve x - 4 -1. Check your solution.
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Example 2 Solve x - 4 -1. Check your
solution. x 4 -1 4 4
Add 4 to each side.
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Example 2 Solve x - 4 -1. Check your
solution. x 4 -1 4 4
Add 4 to each side. x 3
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Example 2 Solve x - 4 -1. Check your
solution. x 4 -1 4 4
Add 4 to each side. x 3 Check x -
4 -1
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Example 2 Solve x - 4 -1. Check your
solution. x 4 -1 4 4
Add 4 to each side. x 3 Check x -
4 -1 3 - 4 ? -1 Replace x with
3 -1 -1 The solution is x
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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 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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1) Solve r 16 -7
- 16 -16 r -23 -23 16 -7

1. Draw the river 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 -3Get 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

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2) Solve x 2 -3
- 2 - 2 x -5 -5 2 -3

1. Draw the river 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

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

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3) Solve 8 m - 3
3 3 11 m 8 11 - 3

1. Draw the river 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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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!
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4) Solve y (-3) 7
y 3 7 3 3 y
10 10 (-3) 7

1. Draw the river 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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Assignment

• P. 112 4-9, 16-21, 30, 33