Solving MultiStep Equations

1
Solving Multi-Step Equations
ALGEBRA 1 LESSON 2-3
(For help, go to Lessons 1-2 and 1-7.)
Simplify each expression. 1. 2n 3n 2. 4 3b
2 5b 3. 9(w 5) 4. 10(b 12) 5. 3(x
4) 6. 5(6 w) Evaluate each expression. 7. 28
a 4a for a 5 8. 8 x 7x for x 3 9. (8n
1)3 for n 2 10. (17 3y) for y 6
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2
Solving Multi-Step Equations
ALGEBRA 1 LESSON 2-3
Solutions
1. 2n 3n (2 3)n 1n n 2. 4 3b 2
5b (3 5)b (4 2) 8b 2 3. 9(w 5)
9w 9(5) 9w 45 4. 10(b 12) 10b
(10)(12) 10b 120 5. 3(x 4) 3(x)
3(4) 3x 12 6. 5(6 w) 5(6) 5w 30
5w 7. 28 a 4a for a 5 28 5 4(5) 28
5 20 23 20 43 8. 8 x 7x for x
3 8 (3) 7(3) 8 (3) 21 5 21
26 9. (8n 1)3 for n 2 (8(2) 1)3 (16
1)3 (15)3 45 10. (17 3y) for y 6
(17 3(6)) (17 18) 35
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Solving Multi-Step Equations
ALGEBRA 1 LESSON 2-3
Solve 3a 6 a 90
4a 6 90 Combine like terms.
4a 6 6 90 6 Subtract 6 from each side.
4a 84 Simplify.
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Solving Multi-Step Equations
ALGEBRA 1 LESSON 2-3
You need to build a rectangular pen in your back
yard for your dog. One side of the pen will be
against the house. Two sides of the pen have a
length of x ft and the width will be 25 ft. What
is the greatest length the pen can be if you have
63 ft of fencing?
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Solving Multi-Step Equations
ALGEBRA 1 LESSON 2-3
(continued)
x 25 x 63
2x 38 Simplify.
x 19
The pen can be 19 ft long.
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6
Solving Multi-Step Equations
ALGEBRA 1 LESSON 2-3
Solve 2(x 3) 8
2x 6 8 Use the Distributive Property.
2x 6 6 8 6 Add 6 to each side.
2x 14 Simplify.
x 7 Simplify.
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7
Solving Multi-Step Equations
ALGEBRA 1 LESSON 2-3
Solve 17
3x2
x5
x 10 Simplify.
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Solving Multi-Step Equations
ALGEBRA 1 LESSON 2-3
Solve 17
3x2
x5
15x 2x 170 Multiply.
17x 170 Combine like terms.
x 10 Simplify.
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9
Solving Multi-Step Equations
ALGEBRA 1 LESSON 2-3
Solve 0.6a 18.65 22.85.
100(0.6a 18.65) 100(22.85) The greatest of
decimal places is two places. Multiply each side
by 100.
100(0.6a) 100(18.65) 100(22.85) Use the
Distributive Property.
60a 1865 2285 Simplify.
60a 1865 1865 2285 1865 Subtract 1865
from each side.
60a 420 Simplify.
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10
Solving Multi-Step Equations
ALGEBRA 1 LESSON 2-3
Solve each equation. 1. 4a 3 a 24 2.
3(x 5) 66 3. 7 4. 0.05x
24.65 27.5
7
17
n3
n4
12
57
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Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-4
(For help, go to Lessons 1-7 and 2-3.)
Simplify. 1. 6x 2x 2. 2x 6x 3. 5x
5x 4. 5x 5x Solve each equation. 5. 4x 3
5 6. x 7 12 7. 2t 8t 1 43 8. 0
7n 4 5n
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Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-4
Solutions
1. 6x 2x (6 2)x 4x 2. 2x 6x (2 6)x
4x 3. 5x 5x (5 5)x 0x 0 4. 5x
5x (5 5)x 0x 0 5. 4x 3 5 6. x
7 12 4x 8 x 5 x 2 x 5 7. 2t
8t 1 43 8. 0 7n 4 5n 6t
1 43 0 12n 4
6t 42 12n 4 t 7 n
1 3
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Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-4
The measure of an angle is (5x 3). Its
vertical angle has a measure of (2x 12). Find
the value of x.
5x 3 2x 12 Vertical angles are congruent.
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Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-4
You can buy a skateboard for 60 from a friend
and rent the safety equipment for 1.50 per hour.
Or you can rent all items you need for 5.50 per
hour. How many hours must you use a skateboard to
justify buying your friends skateboard?
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Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-4
(continued)
60 1.5h 5.5h
You must use your skateboard for more than 15
hours to justify buying the skateboard.
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Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-4
Solve each equation.
a. 6z 8 z 10 7z
6z 8 z 10 7z
6z 8 6z 10 Combine like terms.
6z 8 6z 6z 10 6z Add 6z to each side.
8 10 Not true for any value of z!
This equation has no solution
b. 4 4y 2(2y 2)
4 4y 2(2y 2)
4 4y 4y 4 Use the Distributive Property.
4 4y 4y 4y 4 4y Add 4y to each side.
4 4 Always true!
The equation is true for every value of y, so
the equation is an identity.
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17
Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-4
Solve each equation. 1. 3 2t 7t 4 2. 4n
2(n 1) 3(n 1) 3. 3(1 2x) 4
6x 4. You work for a delivery service. With Plan
A, you can earn 5 per hour plus .75 per
delivery. With Plan B, you can earn 7 per hour
plus .25 per delivery. How many deliveries must
you make per hour with Plan A to earn as much as
with Plan B?
1
no solution
4 deliveries
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