Solving Equations by Using Addition and Subtraction

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Lesson 3-2

• Solving Equations by Using Addition and
  Subtraction

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Objectives

• Solve equations by using addition
• Solve equations by using subtraction

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Vocabulary

• Equivalent equation equations that have the
  same solution
• Solve an equation find all values of the
  variable that make the equation a true statement

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Addition and Subtraction PoE

• Properties of Equality (PoE) are based on the
  concept that as long as you do the same thing to
  both sides of an equation, then you have not
  changed anything.
• Addition PoE
• For any numbers a, b, and c, if a b, then a c
  b c
• You can add the same thing to both sides of an
  equation without changing it.
• Subtraction PoE
• For any numbers a, b, and c, if a b, then a - c
  b - c
• You can subtract the same thing from both sides
  of an equation without changing it.

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Example 1
Solve h 12 -27. Then check your
solution.
To check that 15 is the solution, substitute 15
for h in the original equation.
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Example 2
Solve k 63 92. Then check your solution.
To check that 29 is the solution, substitute 29
for k in the original equation.
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Example 3
Solve c 102 36. Then check your
solution.
To check that 66 is the solution, substitute 66
for c in the original equation.
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Example 4
Write an equation for the problem. Then solve the
equation and check your solution. Fourteen more
than a number is equal to twenty-seven. Find this
number.
Fourteen more than a number is equal to
twenty-seven.
To check that 13 is the solution, substitute 13
for n in the original equation. The solution is
13.
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Example 5
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Example 5 cont
Words The first height plus the additional height
equals 555 feet.
Variables Let a the additional height.
The first height plus the additional height
equals 555.
Answer There were 403 feet added to the
Washington Monument from 1878 to 1888.
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Summary Homework

• Summary
• You can add the same thing to both sides of an
  equation without changing it
• You can subtract the same thing from both sides
  of an equation without changing it
• We can solve equations using these properties
• Homework
• page 132 16-64 even