Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Solve. 1. 3x 102 2. 15 3. z
100 21 4. 1.1 5w 98.6
x 34
y 225
z 121
w 19.5
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A multi-step equation requires more than two
steps to solve. To solve a multi-step equation,
you may have to simplify the equation first by
combining like terms.
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Additional Example 1 Solving Equations That
Contain Like Terms
Solve. 8x 6 3x 2 37
Commutative Property of Addition
8x 3x 6 2 37
11x 4 37 Combine like terms.
4 4 Since 4 is added to 11x,
subtract 4 from both sides to undo the
addition.
11x 33
Since x is multiplied by 11, divide both sides by
11 to undo the multiplication..
x 3
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Check It Out! Example 1
Solve. 9x 5 4x 2 42
Commutative Property of Addition
9x 4x 5 2 42
13x 3 42 Combine like terms.
3 3 Since 3 is added to 13x,
subtract 3 from both sides.
13x 39
Since x is multiplied by 13, divide both sides by
13.
x 3
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If an equation contains fractions, it may help to
multiply both sides of the equation by the least
common denominator (LCD) to clear the fractions
before you isolate the variable.
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Additional Example 2A Solving Equations That
Contain Fractions
Solve.
Multiply both sides by 4.
Distributive Property
Simplify.
5n 7 3
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Additional Example 2A Continued
5n 7 3
7 7 Since 7 is added to 5n, subtract
7 from both sides to undo the
addition.
5n 10
n 2
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Additional Example 2B Solving Equations That
Contain Fractions
Solve.
Multiply both sides by 18, the LCD.
Distributive Property
2
2
9
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Simplify.
1
1
1
1
14x 9x 34 12
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Additional Example 2B Continued
23x 34 12 Combine like terms.
34 34 Since 34 is subtracted from
23x, add 34 to both sides.
23x 46
x 2
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Check It Out! Example 2A
Solve.
Multiply both sides by 4.
Distributive Property
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1
1
Simplify.
1
1
1
3n 5 1
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Check It Out! Example 2A Continued
3n 5 1
5 5 Since 5 is added to 3n,
subtract 5 from both sides.
3n 6
n 2
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Check It Out! Example 2B
Solve.
Multiply both sides by 9, the LCD.
Distributive Property
1
3
3
1
Simplify.
1
1
1
1
5x 3x 13 3
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Check It Out! Example 2B Continued
8x 13 3 Combine like terms.
13 13 Since 13 is subtracted from
8x, add 13 to both sides.
8x 16
x 2
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Additional Example 3 Travel Application
On Monday, David rides his bicycle m miles in 2
hours. On Tuesday, he rides three times as far in
5 hours. If his average speed for the two days is
12 mi/h, how far did he ride on Monday? Round
your answer to the nearest tenth of a mile.
Davids average speed is his total distance for
the two days divided by the total time.

average speed
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Additional Example 3 Continued
Substitute m 3m for total distance and 2 5
for total time.

Simplify.
Multiply both sides by 7.
4m 84
m 21
David rode 21 miles on Monday.
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Check It Out! Example 3
On Saturday, Penelope rode her scooter m miles in
3 hours. On Sunday, she rides twice as far in 7
hours. If her average speed for two days is 20
mi/h, how far did she ride on Saturday? Round
your answer to the nearest tenth of a mile.
Penelopes average speed is her total distance
for the two days divided by the total time.

average speed
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Check It Out! Example 3 Continued
Substitute m 2m for total distance and 3 7
for total time.

Simplify.
Multiply both sides by 10.
3m 200
m ? 66.67
Penelope rode approximately 66.7 miles.
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Lesson Review!
Solve. 1. 6x 3x x 9 33 2. 29 5x 21
3x 3. 5. Linda is paid double
her normal hourly rate for each hour she works
over 40 hours in a week. Last week she worked 52
hours and earned 544. What is her hourly rate?
x 3
x 1
x 28
4.
8.50