3 Mid-Chapter Quiz

Do you know HOW?

Write an inequality that represents each verbal expression or graph.

1. all real numbers y greater than or equal to 12
2. 8 more than a number m is less than 5.
3. 
4. The product of − 3 negative 3  and t is greater than 11.
5. c less than 7 is less than or equal to − 3 . negative 3 .
6. 
7. A cat weighs no more than 8 lb.

Solve each inequality. Graph the solutions.

8. 8 d + 2 < 5 d − 7 8 d plus 2 less than 5 d minus 7
9. 2 n + 1 ≥ − 3 2 n plus 1 greater than or equal to negative 3
10. − 2 x + 7 ≤ 45 negative 2 x plus 7 less than or equal to 45
11. 5 s − 3 + 1 < 8 5 s minus 3 plus 1 less than 8
12. 5 ( 3 p − 2 ) > 50 5 open 3 p minus 2 close greater than 50
13. y 2 < − 3 y over 2 , less than negative 3
14. 6 ≥ − 4 5 n 6 greater than or equal to negative , 4 fifths , n
15. − 1.5 d > 18 negative 1.5 d greater than 18
16. A baseball team wants to collect at least 160 cans of food for an upcoming food drive. Team members brought 42 cans of food on Monday and 65 cans of food on Wednesday. Write and solve an inequality to describe how many cans of food the team must collect on Friday to make or exceed their goal.
17. Suppose you earn $7.25 per hour working part-time for a florist. Write and solve an inequality to find how many full hours you must work to earn at least $125.

Solve each inequality, if possible. If the inequality has no solution, write no solution. If the solutions are all real numbers, write all real numbers .

18. 7 − 6 b ≤ 19 7 minus 6 b less than or equal to 19
19. 15 f + 9 > 3 ( 5 f + 3 ) 15 f plus 9 greater than 3 open 5 f plus 3 close
20. 6 z − 15 ≥ 4 z + 11 6 z minus 15 greater than or equal to 4 z plus 11
21. − 3 ( 4 − m ) ≥ 2 ( 4 m − 14 ) negative 3 open 4 minus m close greater than or equal to 2 open 4 m minus 14 close
22. 8 z + 5 − 2 z ≤ 3 ( 2 z + 1 ) + 2 8 z plus 5 minus 2 z less than or equal to 3 open 2 z plus 1 close plus 2
23. The cheerleaders are making a rectangular banner for a football game. The length of the banner is 30 ft. The cheerleaders can use no more than 96 ft of trim around the outside of the banner. What are the possible widths of the banner?

Do you UNDERSTAND?

24. 1. Error Analysis A student claims that the graph below represents the solutions of the inequality − 3 < x . negative 3 less than x .  What error did the student make?

       

    2. What inequality is actually represented by the graph?

Decide whether the two inequalities in each pair are equivalent. Explain.

25. 36 ≤ − 4 + y ; 40 ≤ y 36 less than or equal to negative 4 plus y semicolon 40 less than or equal to y
26. 9 + b > 24 ; b > 33 9 plus b greater than 24 semicolon b greater than 33
27. m − 1 2 < 3 8 ; m < 7 8 m minus , 1 half , less than , 3 eighths , semicolon m less than , 7 eighths
28. Reasoning A local gym offers a trial membership for 3 months. It discounts the regular monthly fee x by $25. If the total cost of the trial membership is less than $100, you will consider signing up. What inequality can you use to determine whether you should sign up?

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