MATH Integrated Math III  - Unit 4: Inequalities and Absolute Value Equations
For inequality symbols that are non-keyboard entries, write solutions as shown in the following examples:

For the first eight problems, solve for the unknown. State or select the letter of the correct answer.

1) Solve for “z”: 5z – 6 > 14

2) Solve for “x”.

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3) Solve for “x”.

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4) Solve for “r”.

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5) Solve for “x”: 2(x – 3) < 14

6) Solve for “y”.

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7) Solve for “x”.

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8) Solve for “x”.

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For the next four problems, solve the compound inequality. State or select the letter of the correct answer.

9) Solve the compound inequality for “w”: –6(w + 2) > 12 and 17 – 2w < 111

10) Solve the compound inequality for “x”: 10x – 4 < 6 or 4x – 12 < 8

11) Solve the compound inequality for “x”: 8x – 2 > 4 or 3x + 6 < 12

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12) Solve the compound inequality for “x”.

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For the next five problems, select the graph that best fits the solution to the equation or inequality.

13) Choose the best phrase that fits the solution to this equation.

14) Choose the best phrase that fits the solution to this inequality.

15) Choose the best phrase that fits the solution to this inequality.

16) Choose the best phrase that fits the solution to this inequality.

17) Choose the best phrase that fits the solution to this equation.

For the next four problems, solve the absolute value equations.

18) Solve for “x”.

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19) Solve for “x”.

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20) Solve for “x”.

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21) Solve for “x”.

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22) Solve for “x”.

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23) Solve for “x”.

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24) Solve for “m”.

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25) Solve for “x”.

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26) Explain why the graphs of some inequalities include open circles, while others do not?

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27) Describe the two types of compound inequalities.

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28) The right-hand side of the absolute value equation |2x – 3| = _____ is an integer.  Complete the next sentence by filling in the blanks.  If the integer is negative, there is(are) _____ solution(s) for the equation.  If the integer is zero, there is(are) _____ solution(s) for the equation.  If the integer is positive, there is(are) _____ solution(s) for the equation.

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29) Consider this inequality problem. Graph both solutions on a number line. (a) State the union of the two solutions. (b) Now look at the problem again. How could the answer to this problem be determined without solving it algebraically?

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