Equations with Variables on Both Sides

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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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