1. Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-2
(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 = – –x + 7 = 12
7. 2t – 8t + 1 = = –7n + 4 – 5n
2-2

2. Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-2
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 = = –7n + 4 – 5n
–6t + 1 = = –12n + 4
–6t = n = 4
t = –7 n = 1 3
2-2

3. Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-2
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.
5x – 3 – 2x = 2x + 12 – 2x Subtract 2x from each side.
3x – 3 = 12 Combine like terms.
3x – = Add 3 to each side.
3x = 15 Simplify.
= Divide each side by 3.
3x 3
15 3
x = 5 Simplify.
2-2

4. Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-2
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?
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: h = h
2-2

5. Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-2
(continued)
h = 5.5h
h – 1.5h = 5.5h – 1.5h Subtract 1.5h from each side.
60 = 4h Combine like terms.
60 4
4h 4
= Divide each side by 4.
15 = h Simplify.
You must use your skateboard for more than 15 hours to justify buying the skateboard.
2-2

6. Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-2
Solve each equation.
a. –6z + 8 = z + 10 – 7z
–6z + 8 = z + 10 – 7z
–6z + 8 = –6z + 10 Combine like terms.
–6z z = –6z z 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 y Add 4y to each side.
4 = 4 Always true!
The equation is true for every value of y, so the equation is an identity.
2-2

7. Equations with Variables on Both Sides
ALGEBRA 1 LESSON 2-2
Solve each equation.
1. 3 – 2t = 7t n = 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 9 1
no solution
4 deliveries
2-2