Warm Up

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Warm Up Solve. 1. 2x 9x 3x 8 16 2. 4
6x 22 4x
x 1
x 13
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Learn to solve equations with variables on both
sides of the equal sign.
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Some problems produce equations that have
variables on both sides of the equal sign.
Solving an equation with variables on both sides
is similar to solving an equation with a variable
on only one side. You can add or subtract a term
containing a variable on both sides of an
equation.
Copy in Notes! Variables to the left, numbers to
the right!
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Example 1 Solving Equations with Variables on
Both Sides
Solve. 4x 6 x
4x 6 x
x x
Subtract x from both sides.
3x 6 0
Subtract 6 from both sides.
3x -6
Divide both sides by 3
3
3
x -2
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Example 2 Solving Equations with Variables on
Both Sides
Solve. 9b 6 5b 18
9b 6 5b 18
5b 5b
Subtract 5b from both sides.
4b 6 18
6 6
Add 6 to both sides.
4b 24
Divide both sides by 4.
b 6
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Example 3 Solving Equations with Variables on
Both Sides
Solve. 9w 3 9w 7
3 ? 7
No solution. There is no number that can be
substituted for the variable w to make the
equation true.
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Example 4
Solve. 5x 8 x
5x 8 x
x x
Subtract x from both sides.
4x 8 0
Subtract 8 from both sides.
8 -8
Divide both sides by 4.
x -2
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Example 5
Solve. 3b 2 2b 12
3b 2 2b 12
2b 2b
Subtract 2b from both sides.
b 2 12
2 2
Add 2 to both sides.
b 14
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Example 6
Solve. 3w 1 3w 8
1 ? 8
No solution. There is no number that can be
substituted for the variable w to make the
equation true.
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To solve multi-step equations with variables on
both sides, first combine like terms and clear
fractions. Then add or subtract variable terms to
both sides so that the variable occurs on only
one side of the equation. Then use properties of
equality to isolate the variable.
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Example 7 Solving Multi-Step Equations with
Variables on Both Sides
Solve. 10z 15 4z 8 2z - 15
10z 15 4z 8 2z 15
6z 15 2z 7
Combine like terms.
2z 2z
Add 2z to both sides.
8z 15 7
15 15
Add 15 to both sides.
8z 8
Divide both sides by 8.
z 1
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Example 8
Solve. 12z 12 4z 6 2z 32
12z 12 4z 6 2z 32
8z 12 2z 38
Combine like terms.
2z 2z
Add 2z to both sides.
10z 12 38
12 12
Add 12 to both sides.
10z 50
Divide both sides by 10.
z 5
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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Lesson Quiz
Solve. 1. 4x 16 2x 2. 8x 3 15 5x 3.
2(3x 11) 6x 4 4. x x 9 5. An apple
has about 30 calories more than an orange. Five
oranges have about as many calories as 3 apples.
How many calories are in each?
x 8
x 6
no solution
x 36
An orange has 45 calories. An apple has 75
calories.
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Lesson Quiz for Student Response Systems
1. Combine like terms. 4p 14 11p A. p 2 B.
p 7 C. p 14 D. p 15
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Lesson Quiz for Student Response Systems
2. Combine like terms. 3g 6 4g 7 A. g
1 B. g 7 C. g 13 D. g 13
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Lesson Quiz for Student Response Systems
3. Combine like terms. 3(g 2) 7g 18 A. g
2 B. g 3 C. g 3 D. g 2