Download Lesson 7.5

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 = 20
2. 8x – 3x = 35
3. 3b + 2 – b = –18
4. –8 – y + 7y = 40
Check Skills You’ll Need
7-5
Solving Equations With Variables on Both Sides
PRE-ALGEBRA LESSON 7-5
Solutions
1. k + 3k = 20
4k = 20
2. 8x – 3x = 35
5x = 35
4k 20
= 4
4
5x
35
=
5
5
k=5
x=7
3.
3b + 2 – b
(3b – b) + 2
2b + 2
2b + 2 – 2
2b
= –18
= –18
= –18
= –18 – 2
= –20
4.
–8 – y + 7y
–8 + 6y
–8 + 8 + 6y
6y
= 40
= 40
= 40 + 8
= 48
6y
48
=
6
6
2b
–20
=
2
2
y =8
b = –10
7-5
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
6c + 3 = 15
6c + 3 – 3 = 15 – 3
Combine like terms.
Subtract 3 from each side.
6c = 12
Simplify.
6c
12
=
6
6
Divide each side by 6.
c=2
Check
Add 2c to each side.
Simplify.
4c + 3 = 15 – 2c
4(2) + 3 15 – 2(2) Substitute 2 for c.
8 + 3 15 – 4
Multiply.
11 = 11
7-5
Quick Check
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 x = Jenny’s time.
Then
Equation
20
= Steve’s time.
x+5
•
=
x
7-5
15
•
(x + 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.
5x
75
=
5
5
Divide each side by 5.
x = 15
Simplify.
Jenny will catch up with Steve in 15 min.
7-5
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
Solving Equations With Variables on Both Sides
PRE-ALGEBRA LESSON 7-5
Solve each equation.
1. 3 – 2t = 7t + 4
–
2. 18 + 6z = 4z
1
9
3. 2q – 4 = 5 + 5q
–9
4. 7(v – 4) = 3(3 + v) – 1
–3
9
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?
4 deliveries
7-5