Name
Class
1-5
Date
Practice
Form G
Solving Inequalities
Write the inequality that represents the sentence.
1. Four less than a number is greater than 228. x 2 4 + 228
2. Twice a number is at least 15. 2x # 15
3. A number increased by 7 is less than 5. x 1 7 * 5
4. The quotient of a number and 8 is at most 26. x8 K 26
Solve each inequality. Graph the solution.
5. 3(x 1 1) 1 2 , 11 x * 2
!3 !2 !1
0
1
2
6. 5t 2 2(t 1 2) $ 8 t # 4
1
1
8. 3(7a
3
7. 2f(2y 2 1) 1 yg # 5( y 1 3) y " 17
1
2
5
6
7
2 1) # 2a 1 7 a " 22
10. 22(w 2 7) 1 3 . w 2 1 w * 6
9. 5 2 2(n 1 2) # 4 1 n n # 21
0
4
3
19 20 21 22 23 24 25
14 15 16 17 18 19 20
!3 !2 !1
2
3
3
4
5
6
7
8
9
Solve each problem by writing an inequality.
11. Geometry The length of a rectangular yard is 30 meters. The perimeter is at
most 90 meters. Describe the width of the yard. at most 15 m
12. Geometry A piece of rope 20 feet long is cut from a longer piece that is at least
32 feet long. The remainder is cut into four pieces of equal length. Describe
the length of each of the four pieces. at least 3 ft
13. A school principal estimates that no more than 6% of this year’s senior class
will graduate with honors. If 350 students graduate this year, how many will
graduate with honors? no more than 21 students
14. Two sisters drove 144 miles on a camping trip. They averaged at least 32 miles
per gallon on the trip. Describe the number of gallons of gas they used.
at most 4.5 gal
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43
Name
1-5
Class
Date
Practice (continued)
Form G
Solving Inequalities
Is the inequality always, sometimes, or never true?
15. 3(2x 1 1) . 5x 2 (2 2 x) always true
16. 2(x 2 1) $ x 1 7 sometimes true
17. 7x 1 2 # 2(2x 2 4) 1 3x never true
18. 5(x 2 3) , 2(x 2 9) sometimes true
Solve each compound inequality. Graph the solution.
19. 3x . 26 and 2x , 6 x + 22 and x * 3
!3 !2 !1
0
1
2
3
20. 4x $ 212 and 7x # 7 x # 23 and x " 1
!3 !2 !1
0
1
2
3
21. 5x . 220 and 8x # 32 x + 24 and x " 4
!6 !4 !2
0
2
4
6
22. 6x , 212 or 5x . 5 x * 22 or x + 1
!3 !2 !1
0
1
2
3
23. 6x # 218 or 2x . 18 x " 23 or x + 9
!6 !3
0
3
6
9
12
24. 2x . 3 2 x or 2x , x 2 3 x + 1 or x * 23
!4 !3 !2 !1
0
1
2
Solve each problem by writing and solving a compound inequality.
25. A student believes she can earn between $5200 and $6250 from her summer
job. She knows that she will have to buy four new tires for her car at $90 each.
She estimates her other expenses while she is working at $660. How much can
the student save from her summer wages? between $4180 and $5230
26. Before a chemist can combine a solution with other liquids in a laboratory,
the temperature of the solution must be between 39°C and 52°C. The chemist
places the solution in a warmer that raises the temperature 6.5°C per hour. If
the temperature is originally 0°C, how long will it take to raise the temperature
to the necessary range of values? between 6 and 8 h
27. The Science Club advisor expects that between 42 and 49 students will attend
the next Science Club field trip. The school allows $5.50 per student for
sandwiches and drinks. What is the advisor’s budget for food for the trip?
between $231 and $269.50
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44