5-2 Solving Equations with Variables on Each Side
Solve each equation. Check your solution.
1. x + 6 = 3x
SOLUTION: Check:
2. 4y = 2y – 10
SOLUTION: Check:
3. 7z – 4 = 12 + 3z
SOLUTION: Check:
eSolutions Manual - Powered by Cognero
Page 1
5-2 Solving Equations with Variables on Each Side
3. 7z – 4 = 12 + 3z
SOLUTION: Check:
4. 10t – 3 = t + 15
SOLUTION: Check:
5. 28 – x = 3x – 84
SOLUTION: eSolutions Manual - Powered by Cognero
Check:
Page 2
5-2 Solving Equations with Variables on Each Side
5. 28 – x = 3x – 84
SOLUTION: Check:
6. 2p – 7 = 13 – 8p
SOLUTION: Check:
7. MONEY An Internet movie rental company charges a yearly membership fee of $50 plus $1.99 per DVD rental.
Your neighborhood rental store has no membership fee and charges $3.99 per DVD rental. Write and solve an
equation to find the number of DVDs so the cost for each will be the same.
SOLUTION: yearly membership fee + cost per DVD × number of DVDs = cost per DVD × number of DVDs
Let m = number of DVDs.
eSolutions Manual - Powered by Cognero
So, the cost for each will be the same for 25 DVDs.
Page 3
5-2 Solving Equations with Variables on Each Side
7. MONEY An Internet movie rental company charges a yearly membership fee of $50 plus $1.99 per DVD rental.
Your neighborhood rental store has no membership fee and charges $3.99 per DVD rental. Write and solve an
equation to find the number of DVDs so the cost for each will be the same.
SOLUTION: yearly membership fee + cost per DVD × number of DVDs = cost per DVD × number of DVDs
Let m = number of DVDs.
So, the cost for each will be the same for 25 DVDs.
Solve each equation. Check your solution.
8. 2x + 3 = x
SOLUTION: Check:
9. 8 – v = 7v
SOLUTION: Check:
eSolutions Manual - Powered by Cognero
Page 4
5-2 Solving Equations with Variables on Each Side
9. 8 – v = 7v
SOLUTION: Check:
10. 8 – 2c = 2c
SOLUTION: Check:
11. q – 2 = –q + 1
SOLUTION: Check:
eSolutions Manual - Powered by Cognero
Page 5
5-2 Solving Equations with Variables on Each Side
11. q – 2 = –q + 1
SOLUTION: Check:
12. –2 + x = –2 + 2x
SOLUTION: Check:
13. 14 + 3a = –2a – 1
SOLUTION: eSolutions Manual - Powered by Cognero
Check:
Page 6
5-2 Solving Equations with Variables on Each Side
13. 14 + 3a = –2a – 1
SOLUTION: Check:
14. 12p = p + 14 + p
SOLUTION: Check:
15. 5b – 4b = 6b – 2
SOLUTION: eSolutions Manual - Powered by Cognero
Check:
Page 7
Check:
5-2 Solving Equations with Variables on Each Side
15. 5b – 4b = 6b – 2
SOLUTION: Check:
16. CAR RENTALS Use the table below to write and solve an equation to find the number of miles a rental car must
be driven for each option to cost the same for one day.
SOLUTION: cost per day + cost per mile × number of miles = cost per day + cost per mile × number of miles
So, a rental car must be driven 75 miles for each option to cost the same for one day.
17. MUSIC DOWNLOADS Denzel is comparing websites for downloading music. One charges a $5 membership fee
plus $0.50 per song. Another charges $1.00 per song, but has no membership fee. Write and solve an equation to
find how many songs Denzel would have to buy to spend the same amount at both websites.
SOLUTION: membership fee + cost per song × number of songs = cost per song × number of songs
Let s = number of songs.
eSolutions Manual - Powered by Cognero
Page 8
5-2 Solving Equations with Variables on Each Side
So, a rental car must be driven 75 miles for each option to cost the same for one day.
17. MUSIC DOWNLOADS Denzel is comparing websites for downloading music. One charges a $5 membership fee
plus $0.50 per song. Another charges $1.00 per song, but has no membership fee. Write and solve an equation to
find how many songs Denzel would have to buy to spend the same amount at both websites.
SOLUTION: membership fee + cost per song × number of songs = cost per song × number of songs
Let s = number of songs.
So, Dezel would have to buy 10 songs to spend the same amount at both websites.
Solve each equation. Check your solution.
18. 3.2 + 0.3x = 0.2x + 1.4
SOLUTION: Check:
19. 0.4x = 2x + 1.2
SOLUTION: Check:
eSolutions Manual - Powered by Cognero
Page 9
5-2 Solving Equations with Variables on Each Side
19. 0.4x = 2x + 1.2
SOLUTION: Check:
20. 7.2 – 3c = 2c – 2
SOLUTION: Check:
21. 3 – 3.7b = 10.3b + 10
SOLUTION: eSolutions Manual - Powered by Cognero
Check:
Page 10
5-2 Solving Equations with Variables on Each Side
21. 3 – 3.7b = 10.3b + 10
SOLUTION: Check:
22. x+6=
x + 28
SOLUTION: Check:
eSolutions Manual - Powered by Cognero
Page 11
5-2 Solving Equations with Variables on Each Side
22. x+6=
x + 28
SOLUTION: Check:
23. x – 8 = 20 +
x
SOLUTION: eSolutions Manual - Powered by Cognero
Check:
Page 12
5-2 Solving Equations with Variables on Each Side
23. x – 8 = 20 +
x
SOLUTION: Check:
24. SHOPPING Gabriella bought some school supplies for $48 and then bought 3 CDs. Min did not buy any school
supplies but bought 7 CDs. All the CDs cost the same amount and they both spent the same amount of money.
Write and solve an equation to find the cost of one CD.
SOLUTION: school supplies + 3 × cost of a CD = 7 × cost of a CD
Let c = the cost of a CD.
So, the cost of one CD is $12.
25. FINANCIAL LITERACY One cell phone company charges $19.95 a month plus $0.21 per text message, and a
second company charges $24.95 per month plus $0.16 per text message. For how many text messages is the cost of
the plans the same?
SOLUTION: monthly fee + cost per text message × number of text messages = monthly fee + cost per text message × number of
Page 13
text messages
Let t = number of text messages.
eSolutions Manual - Powered by Cognero
5-2 Solving Equations with Variables on Each Side
So, the cost of one CD is $12.
25. FINANCIAL LITERACY One cell phone company charges $19.95 a month plus $0.21 per text message, and a
second company charges $24.95 per month plus $0.16 per text message. For how many text messages is the cost of
the plans the same?
SOLUTION: monthly fee + cost per text message × number of text messages = monthly fee + cost per text message × number of
text messages
Let t = number of text messages.
So, the cost of the plans is the same for 100 text messages.
26. AGES Five years ago Ang was
as old as Paula. Now he is as old as Paula. Complete the table shown below.
Then use the table to write and solve an equation to find their current ages.
SOLUTION: To complete the table, add 5 to Ang’s age 5 years ago.
Student
5 years ago
Now
Ang
a
a +5
Paula
a
a+5
Because, Ang is now
as old as Paula, use the following equation to find both of their current ages.
eSolutions Manual - Powered by Cognero
Page 14
5-2 Solving Equations with Variables on Each Side
So, the cost of the plans is the same for 100 text messages.
26. AGES Five years ago Ang was
as old as Paula. Now he is as old as Paula. Complete the table shown below.
Then use the table to write and solve an equation to find their current ages.
SOLUTION: To complete the table, add 5 to Ang’s age 5 years ago.
Student
5 years ago
Now
Ang
a
a +5
Paula
a
a+5
Because, Ang is now
as old as Paula, use the following equation to find both of their current ages.
27. COASTLINE Florida’s coastline is 118 miles shorter than four times the coastline of Texas. It is also 983 miles
longer than the coastline of Texas. Find the lengths of the coastlines of Florida and Texas.
SOLUTION: four × coastline of Texas – 118 = coastline of Texas + 983
Let c = coastline of Texas.
eSolutions Manual - Powered by Cognero
Page 15
5-2 Solving Equations with Variables on Each Side
27. COASTLINE Florida’s coastline is 118 miles shorter than four times the coastline of Texas. It is also 983 miles
longer than the coastline of Texas. Find the lengths of the coastlines of Florida and Texas.
SOLUTION: four × coastline of Texas – 118 = coastline of Texas + 983
Let c = coastline of Texas.
So, the coastline of Texas is 367 miles and the coastline of Florida is 1350 miles.
28. GEOMETRY Use the square shown below.
a. What is the value of x?
b. Find the length of each side of the square.
SOLUTION: a. Because all sides of a square are equal, you can use the equation 4x = 2x + 10 to find x.
So, x = 5.
b. To find the length of each side, replace x with 5 in one of the expressions for side length.
So, the length of each side of the square is 20 units.
29. LANDSCAPE Jamie is going to fence the rectangular and triangular sections of grass shown below. The
perimeters of the two sections are now equal. If w represents the width of the rectangle, how could you find the
lengths of the sides of the rectangle and of the triangle? Justify your response and use your method to solve the
problem.
eSolutions Manual - Powered by Cognero
Page 16
SOLUTION: Sample answer: Use the information in the figure to write and solve an equation. To find the perimeter of a figure,
So, x = 5.
b. To find the length of each side, replace x with 5 in one of the expressions for side length.
5-2 Solving Equations with Variables on Each Side
So, the length of each side of the square is 20 units.
29. LANDSCAPE Jamie is going to fence the rectangular and triangular sections of grass shown below. The
perimeters of the two sections are now equal. If w represents the width of the rectangle, how could you find the
lengths of the sides of the rectangle and of the triangle? Justify your response and use your method to solve the
problem.
SOLUTION: Sample answer: Use the information in the figure to write and solve an equation. To find the perimeter of a figure,
find the sum of the lengths of the sides. So, the perimeter of the rectangle can be represented by the expression w +
w + 40 + w + w + 40 or 4w + 80. The perimeter of the triangle can be represented by the expression w + 45 + w +
45 + w + 45 or 3w + 135. Because the perimeters of the two sections are equal, set the two expressions equal to
each other and solve for w.
For the rectangle, the width is 55 feet and the length is 95 feet. For the triangle, the sides are 100 feet.
eSolutions Manual - Powered by Cognero
Page 17