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Equations with Variables on Both Sides

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ALGEBRA 1 LESSON 2-4

(For help, go to Lessons 1-7 and 2-3.)

Simplify.

1.6x – 2x2.2x – 6x3.5x – 5x4.–5x + 5x

Solve each equation.

5.4x + 3 = –56.–x + 7 = 12

7.2t – 8t + 1 = 438.0 = –7n + 4 – 5n

2-4

ALGEBRA 1 LESSON 2-4

Solutions

1.6x – 2x=(6 – 2)x = 4x2.2x – 6x= (2 – 6)x = –4x

3.5x – 5x=(5 – 5)x = 0x = 04.–5x + 5x=(–5 + 5)x = 0x = 0

5.4x + 3=–56.–x + 7=12

4x=–8–x=5

x=–2x=–5

7.2t – 8t + 1=438.0=–7n + 4 – 5n

–6t + 1=430=–12n + 4

–6t=4212n=4

t=–7n=

1

3

2-4

5x – 3 – 2x=2x + 12 – 2xSubtract 2x from each side.

3x – 3=12Combine like terms.

3x – 3+ 3=12 + 3Add 3 to each side.

3x=15Simplify.

=Divide each side by 3.

3x3

153

x=5Simplify.

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 + 12Vertical angles are congruent.

2-4

Relate: cost of plus equipment equals skateboard and equipment

friend’s rental rental

skateboard

Define: let h = the number of hours you must skateboard

Write: 60 + 1.5 h = 5.5 h

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 friend’s skateboard?

2-4

60 + 1.5h – 1.5h=5.5h – 1.5hSubtract 1.5h from each side.

60=4hCombine like terms.

604

4h4

=Divide each side by 4.

15=hSimplify.

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.

2-4

ALGEBRA 1 LESSON 2-4

Solve each equation.

a.–6z + 8=z + 10 – 7z

–6z + 8=z + 10 – 7z

–6z + 8=–6z + 10Combine like terms.

–6z + 8 + 6z=–6z + 10 + 6zAdd 6z to each side.

8=10Not 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 + 4Use the Distributive Property.

4 – 4y + 4y=–4y + 4 + 4yAdd 4y to each side.

4=4Always true!

The equation is true for every value of y, so the equation is an identity.

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