### About Compound Inequalities:

A compound inequality is an inequality that is linked with a connective word such as 'and' or 'or'. The solution for a compound inequality with ‘and’ is the intersection of the two solutions sets. The solution for a compound inequality with ‘or’ is the union of the two solutions sets.

Test Objectives

- Demonstrate the ability to solve a compound inequality with "and"
- Demonstrate the ability to solve a compound inequality with "or"
- Demonstrate the ability to graph the solution for a compound inequality

#1:

Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.

a) 3r - 7 ≤ r + 7 and 11r + 7 > 6r - 3

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#2:

Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.

a) -2 - 12n ≤ -15n - 14 and 2n + 9 ≤ n + 2

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#3:

Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.

a) -2(6 - 7x) < 16 + 7x and 13x + 7 ≥ 12x + 13

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#4:

a) 2(2 + 4n) < -12 or 9n + 19 > 46

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#5:

a) 7 - 20v ≥ 67 or 8v + 9 ≥ -95

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Written Solutions:

#1:

Solutions:

a) -2 < r ≤ 7

(-2,7]

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#2:

Solutions:

a) n ≤ -7

(-∞,-7)

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#3:

Solutions:

a) No solution

∅

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#4:

Solutions:

a) n < -2 or n > 3

(-∞,-2) ∪ (3,∞)

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#5:

Solutions:

a) All real numbers

(-∞,∞)