Page 1 of 4
Solving Two-Step Equations
BEFORE
Now
WHY?
You solved one-step equations.
You’ll solve two-step equations.
So you can find the width of a
basketball court, as in Ex. 25.
Work backward to solve the equation 3x 1 5.
Word Watch
Review Words
inverse operations, p. 327
1 Draw a box model to represent the
equation 3x 1 5.
2 Rewrite the model using inverse
operations. Work from right to left.
To undo adding 1, subtract 1. To undo
multiplying by 3, divide by 3.
3 Solve the equation. Because
5 1 6 and 6 (3) 2,
you know that x 2. So, the solution of
the equation 3x 1 5 is 2.
(3)
1
?
x
?
x
(3)
2
(3)
1
6
1
5
5
5
Use a box model to solve the equation.
1. 6x 1 7
2. 2x 3 11
3. 4x 5 7
Using Inverse Operations Two-step equations, like 3x 1 5
above, involve two operations and require using two inverse operations,
in succession, to solve.
EXAMPLE
with
1
Solving a Two-Step Equation
Solve 5x 6 21.
Solving
Don’t forget to check your
solution by substituting
back into the original
equation.
5x 6 21
5x 6 6 21 6
Chapter 7
Add 6 to each side.
5x 15
Simplify.
5x
15
5
5
Divide each side by 5.
x 3
342
Write original equation.
Equations, Inequalities, and Functions
Simplify.
Page 2 of 4
EXAMPLE
2
Solving a Two-Step Equation
c
3
Solve 13 0.
c
13 0
3
Write original equation.
c
13 13 0 13
3
Subtract 13 from each side.
c
13
3
Simplify.
3c 3 3(13)
Multiply each side by 3.
c 39
Your turn now
Solve the equation. Check your solution.
x
2. 10 10
2
1. 6d 9 15
EXAMPLE
3
Simplify.
m
3. 7 7
4
Writing and Solving a Two-Step Equation
Bicycle Repair Your bicycle needs to be fixed. A mechanic charges $40
for each hour of labor, and the new parts cost $35. The total cost of fixing
the bicycle is $95. How long did it take the mechanic to fix the bicycle?
Solution
Write a verbal model. Let n represent the number of hours of labor.
Cost of new
Cost of labor
p
parts
per hour
35
40
35 40n 95
35 35 40n 95 35
Number of
hours of labor
p
n
95
Write equation.
Subtract 35 from each side.
40n 60
Simplify.
40n
60
40
40
Divide each side by 40.
n 1.5
Total cost
Simplify.
ANSWER The mechanic took 1.5 hours to fix the bicycle.
Lesson 7.5
Solving Two-Step Equations
343
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 711
Getting Ready to Practice
1. Vocabulary Which properties would you use to solve the equation
5x 3 12?
Solve the equation. Check your solution.
2. 3x 2 4
x
3. 7x 5 9 4. 2 7
9
x
5. 6 5
5
6. Internet Shopping You have $65 to spend on party favors. On the
Internet, you find visors that cost $6 each. The shipping and handling
charge is $5 for the entire order. How many visors can you buy?
Practice and Problem Solving
7. Put the steps for solving the equation 7x 10 3 in order.
with
Example
1
2
3
Homework
Exercises
7–19, 26–31
7–19, 26–31
22–23, 25
A. Add 10 to each side.
B. Check your answer.
C. Write original equation.
D. Divide each side by 7.
Solve the equation. Check your solution.
8. 9y 4 14
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
9. 7b 7 42
10. 13p 8 5
11. 29 2x 13
e
12. 3 3
9
13. 129 12b 15
f
14. 20 20
12
3
15. w 14 10
8
16. 77 t 55
d
17. 8 2
5
18. 0 2.5y 20
19. 3(x 1) 12
Write the verbal sentence as an equation. Then solve the equation.
20. Twice a number subtracted from 7 is 11.
21. 8 added to 4 times a number equals 4.
22. Souvenirs You are sightseeing in Chicago and have $20 to spend on
with
souvenirs. You buy a baseball cap for $8. You want to buy keychains to
bring home to your friends. How many keychains can you buy if each
one costs $1.50?
Review
Need help with time
conversions? See p. 697.
344
Chapter 7
23. Walking You jog at a speed of 6 miles per hour for 20 minutes, and you
walk at a speed of 4 miles per hour for t minutes. If your combined
jogging and walking distance is 3 miles, for how long did you walk?
Equations, Inequalities, and Functions
Page 4 of 4
24. Critical Thinking Write a two-step equation whose solution is 2.
25. Basketball The length of a basketball court is 84 feet, and the
perimeter is 268 feet. What is the width of the basketball court?
Solve the equation. Check your solution.
f
26. 1.2 30
6
z
29. 5 12
0.25
11
27. 6w 7
2
30. 3r 6 9r 24
5
8
28. 2x 13
13
2
5
31. s 1 3
6
32. Challenge Find two solutions of the equation 3x 10 20.
33. Test Average On the first three 100 point tests of the grading period,
your scores were 85, 92, and 76. What score do you need to get on the
fourth 100 point test to have a mean score of 85?
Mixed Review
Copy and complete the statement using <, >, or . (Lessons 4.5, 4.6)
3
2
34. _?_ 5
3
1
1
35. _?_ 8
9
5
3
36. _?_ 2
4
1
7
37. 3 _?_ 2
2
Solve the equation. Check your solution. (Lesson 7.4)
38. 6w 72
39. 7.5x 37.5
y
40. 9
22
z
41. 8.5
4.2
Basic Skills Use the Venn diagram to
tell whether the statement is true or false.
Owns
a cat
42. Tina owns a cat.
43. Kevin does not own a dog.
John
Owns
a dog
Kevin
Tina
44. Kevin and John both own cats.
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
45. Multiple Choice A shoe store is having a sale, and all shoes are half off
the original price. You use a coupon for an additional $5 off the sale
price, so that you pay $17 for a pair of shoes. What is the original price?
A. $11
B. $24
C. $39
D. $44
46. Short Response You are using a word processor to create a table.
The table will be 5 inches wide. The first column of the table will be
3 inches wide, and the remaining 4 columns will have equal width.
How wide should you make each of the 4 columns of equal width?
Lesson 7.5
Solving Two-Step Equations
345