1. Solving Equations With Variables on Both Sides
PRE-ALGEBRA LESSON 7-5
(For help, go to Lesson 7-2.)
Solve each equation.
1. k + 3k = x – 3x = 35
3. 3b + 2 – b = – –8 – y + 7y = 40
Check Skills You’ll Need
7-5

2. Solving Equations With Variables on Both Sides
PRE-ALGEBRA LESSON 7-5
Solutions
1. k + 3k = x – 3x = 35
4k = x = 35
k = x = 7
b + 2 – b = – –8 – y + 7y = 40
(3b – b) + 2 = – –8 + 6y = 40
2b + 2 = – – y =
2b + 2 – 2 = –18 – y = 48
2b = –20
y = 8
b = –10 = 20 4 4k 35 5 5x 48 6 6y
–20 2 2b
7-5

3. Solving Equations With Variables on Both Sides
PRE-ALGEBRA LESSON 7-5
Solve 4c + 3 = 15 – 2c.
4c + 3 = 15 – 2c
4c + 2c + 3 = 15 – 2c + 2c
Add 2c to each side.
6c + 3 = 15
Combine like terms.
6c + 3 – 3 = 15 – 3
Subtract 3 from each side.
6c = 12
Simplify.
c = 2
Simplify.
Divide each side by 6. = 6c 6 12
Check 4c + 3 = 15 – 2c
4(2) – 2(2)  
– 4
11 = 11
Substitute 2 for c.
Multiply.
Quick Check
7-5

4. Solving Equations With Variables on Both Sides
PRE-ALGEBRA LESSON 7-5
Steve types at a rate of 15 words/min and Jenny types at a rate of 20 words/min. Steve and Jenny are both typing the same document, and Steve starts 5 min before Jenny. How long will it take Jenny to catch up with Steve?
words Jenny types = words Steve types
Words
20 words/min •
Jenny’s time
= 15 words/min •
Steve’s time
Let = Jenny’s time. x
Then
x + 5
= Steve’s time.
Equation
20 • x
= •
(x + 5)
7-5

5. Solving Equations With Variables on Both Sides
PRE-ALGEBRA LESSON 7-5
(continued)
20x = 15(x + 5)
20x = 15x + 75
Use the Distributive Property.
20x – 15x = 15x – 15x + 75
Subtract 15x from each side.
5x = 75
Combine like terms.
Divide each side by 5. = 5x 5 75
x = 15
Simplify.
Jenny will catch up with Steve in 15 min.
7-5

6. Solving Equations With Variables on Both Sides
PRE-ALGEBRA LESSON 7-5
(continued)
Check   Test the result.
At 20 words/min for 15 min, Jenny types 300 words.
Steve’s time is five min longer. He types for 20 min.
At 15 words/min for 20 min, Steve types 300 words.
Since Jenny and Steve each type 300 words, the answer checks.
Quick Check
7-5

7. Solving Equations With Variables on Both Sides
PRE-ALGEBRA LESSON 7-5
Solve each equation.
1. 3 – 2t = 7t z = 4z
3. 2q – 4 = 5 + 5q 4. 7(v – 4) = 3(3 + v) – 1
5. 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 to earn the same amount from either plan? 1 9 – –9 –3 9
4 deliveries
7-5