Name ________________________________________ Date __________________ Class __________________
LESSON
7-3
Solving Two-Step Inequalities
Practice and Problem Solving: A/B
Fill in the blanks to show the steps in solving the inequality.
1. 3x − 5 < 19
2. −2x + 12 < −4
3x − 5 + ______ < 19 + ______
−2x + 12 − ______ < −4 − ______
3x < _________________
−2x < _________________
3x ÷ ______ < ______ ÷ ______
−2x ÷ ______ > ______ ÷ ______
x < _________________
x > _________________
3. Why do the inequality signs stay the same in the last two steps of Exercise 1?
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4. Why is the inequality sign reversed in the last two steps of Exercise 2?
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Solve the inequalities. Show your work.
5. −7d + 8 > 29
6. 12 − 3b < 9
7.
z
− 6 ≥ −5
7
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8. Fifty students are trying to raise at least $12,500 for a class trip. They
have already raised $1,250. How much should each student raise, on
average, in order to meet the goal? Write and solve the two-step
inequality for this problem.
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9. At the end of the day, vegetables at Farm Market sell for $2.00 a
pound, and a basket costs $3.50. If Charlene wants to buy a basket
and spend no more than $10.00 total, how many pounds of vegetables
can she buy? Write and solve the inequality.
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3. x + 5 < 7
12 − 3b < 9
6.
4. n − 10 > 30
12 − 12 −3b < 9 − 12
5. 5n + 2 ≥ 3
−3b < −3
6. 2n − 6 ≤ 17
b>1
7. Twelve times the number of cars she
washes minus $50 for her savings must
be greater than or equal to $100. Twelve
times the number of cars, n, is 12n.
Subtract $50 for her savings:
12n − 50. This has to be at least $100,
so 12n − 50 ≥ 100.
z
− 6 + 6 ≥ −5 + 6
7
z
≥1
7
z≥7
8. 49 times the number of games plus $400
for the video player must be less than or
equal to the saved $750, so
49n + 400 ≤ 750 or 750 ≥ 400 + 49x.
8. 50x + 1,250 ≥ 12,500 or x ≥ $225
9. 2n + 3.50 ≤10
2n ≤ 6.50
9. The number of samples saved for display,
50, plus the distribution at the rate of
25 per hour must be less than or equal to
250, so 50 + 25t ≤ 250.
n ≤ 3.25
She can buy no more than 3.25 lb.
Practice and Problem Solving: C
Reteach
1. −5a > 15; −5a + 2 > 15 + 2
1. 3n; 5 −; 3n − 5; 3n − 5 > −8
2. 3b ≤ 3; 3b + 4 ≥ 3 + 4; 3b ≥ 7
2. 5n; + 13; 5n + 13; 5n + 13 ≤ 30
3. 3x + 7 > 12; 3x + 12 > 7; 7 + 12 > 3x
Reading Strategies
4. x >
1
1. (a + 6) ≥ 20
2
5
5
19
; x > − ;x <
3
3
3
5. All three solutions overlap at
5
19
< x < , which gives the common
3
3
solution for all three inequalities.
2. 12 + 3b ≤ −11
3. 2c − 8 < 5
Success for English Learners
6. Answers will vary. Sample answer:
1. Sample answer: Five minus two times a
number is greater than the opposite of four.
“The opposite of three is no less than a
third of the difference of 6 and a number.”
x ≥ 15
7. Answers will vary. Sample answer:
2. 3n − 7 ≤ −10
LESSON 7-3
“Four times the sum of one and twice a
number is less than the opposite of one
9
half.” x < − .
16
Practice and Problem Solving: A/B
1. 5, 5; 24; 3, 24, 3; 8
2. 12, 12; −16; −2, −16, −2; 8
3. Because you are dividing by a
positive number.
Practice and Problem Solving: D
1. y > 2
4. Because you are dividing by a
negative number.
5.
z
− 6 ≥ −5
7
7.
2. d ≤ −4
−7d + 8 > 29
−7d + 8 − 8 > 29 − 8
3. r > −12
−7d > 21
d < −3
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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