Learn to solve equations using addition and subtraction'

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Learn to solve equations using addition and
subtraction.
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Vocabulary
equation solve solution inverse operation isolate
the variable Addition Property of
Equality Subtraction Property of Equality
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An equation uses an equal sign to show that two
expressions are equal. All of these are equations.
3 8 11
r 6 14
24 x 7
To solve an equation, find the value of the
variable that makes the equation true. This value
of the variable is called the solution of the
equation.
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Additional Example 1 Determining Whether a
Number is a Solution of an Equation
Determine which value of x is a solution of the
equation. x 8 15 x 5, 7, or 23
Substitute each value for x in the equation.
Substitute 5 for x.
?
So 5 is not solution.
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Additional Example 1 Continued
Determine which value of x is a solution of the
equation. x 8 15 x 5, 7, or 23
Substitute each value for x in the equation.
Substitute 7 for x.
?
So 7 is a solution.
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Additional Example 1 Continued
Determine which value of x is a solution of the
equation. x 8 15 x 5, 7, or 23
Substitute each value for x in the equation.
Substitute 23 for x.
?
So 23 is not a solution.
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Try This Example 1
Determine which value of x is a solution of the
equation. x 4 13 x 9, 17, or 27
Substitute each value for x in the equation.
Substitute 9 for x.
?
So 9 is not a solution.
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Try This Example 1 Continued
Determine which value of x is a solution of the
equation. x 4 13 x 9, 17, or 27
Substitute each value for x in the equation.
Substitute 17 for x.
?
So 17 is a solution.
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Try This Example 1 Continued
Determine which value of x is a solution of the
equation. x 4 13 x 9, 17, or 27
Substitute each value for x in the equation.
Substitute 27 for x.
?
So 27 is not a solution.
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Addition and subtraction are inverse operations,
which means they undo each other.
To solve an equation, use inverse operations to
isolate the variable. This means getting the
variable alone on one side of the equal sign.
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To solve a subtraction equation, like y ? 15 7,
you would use the Addition Property of Equality.
You can add the same number to both sides of an
equation, and the statement will still be true.
2 3 5
x y
x y
2 7 9
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There is a similar property for solving addition
equations, like x 9 11. It is called the
Subtraction Property of Equality.
You can subtract the same number from both sides
of an equation, and the statement will still be
true.
4 7 11
x y
x y
4 4 8
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Additional Example 2A Solving Equations Using
Addition and Subtraction Properties
Solve.
A. 10 n 18
Subtract 10 from both sides.
10 n 18
10
10
0 n 8
Identity Property of Zero 0 n n.
n 8
Check
10 n 18
?
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Additional Example 2B Solving Equations Using
Addition and Subtraction Properties
Solve.
B. p 8 9
Add 8 to both sides.
p 8 9
8
8
p 0 17
Identity Property of Zero p 0 p.
p 17
Check
p 8 9
?
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Additional Example 2C Solving Equations Using
Addition and Subtraction Properties
Solve.
C. 22 y 11
Add 11 to both sides.
22 y 11
11
11
33 y 0
Identity Property of Zero y 0 0.
33 y
Check
22 y 11
?
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Try This Example 2A
Solve.
A. 15 n 29
Subtract 15 from both sides.
15 n 29
15
15
0 n 14
Identity Property of Zero 0 n n.
n 14
Check
15 n 29
?
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Try This Example 2B
Solve.
B. p 6 7
Add 6 to both sides.
p 6 7
6
6
p 0 13
Identity Property of Zero p 0 p.
p 13
Check
p 6 7
?
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Try This Example 2C
Solve.
C. 44 y 23
Add 23 to both sides.
44 y 23
23
23
67 y 0
Identity Property of Zero y 0 0.
67 y
Check
44 y 23
?
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Additional Example 3A
A. Jan took a 34-mile trip in her car, and the
odometer showed 16,550 miles at the end of the
trip. What was the original odometer reading?




34
x
Solve
16,550
x 34 16,550
34
34
Subtract 34 from both sides.
x 0 16,516
x 16,516
The original odometer reading was 16,516 miles.
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Additional Example 3B
B. From 1980 to 2000, the population of a town
increased from 895 residents to 1125 residents.
What was the increase in population during that
20-year period?




n
895
Solve
1125
895 n 1125
895
895
Subtract 895 from both sides.
0 n 230
n 230
The increase in population was 230.
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Try This Example 3A
A. Isabelle earned 27 interest and now has a
balance of 535 in the bank. What was her balance
before interest was added?




27
x
Solve
535
x 27 535
27
27
Subtract 27 from both sides.
x 0 508
x 508
Isabelle had a balance of 508 before interest
was added.
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Try This Example 3B
B. From June to July, the water level in a lake
has increased from 472 feet to 502 feet. What was
the increase in water level during that 1-month
period?




n
472
Solve
502
472 n 502
472
472
Subtract 472 from both sides.
0 n 30
n 30
The increase in water level was 30 feet.
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Lesson Quiz
Determine which value of x is a solution of the
equation. 1. x 9 17 x 6, 8, or 26 2. x
3 18 x 15, 18, or 21 Solve. 3. a 4
22 4. n 6 39 5. The price of your favorite
cereal is now 4.25. In prior weeks the price was
3.69. Write and solve an equation to find n, the
increase in the price of the cereal.
8
21
a 18
n 45
3.69 n 4.25 0.56