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 solution sets. The solution for a compound inequality with ‘or’ is the union of the two solution 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 in interval notation, graph.
a) $$3r - 7 ≤ r + 7$$ $$\text{and}$$ $$11r + 7 > 6r - 3$$
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#2:
Instructions: Solve each inequality, write in interval notation, graph.
a) $$-2 - 12n ≤ -15n - 14$$ $$\text{and}$$ $$2n + 9 ≤ n + 2$$
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#3:
Instructions: Solve each inequality, write in interval notation, graph.
a) $$-2(6 - 7x) < 16 + 7x$$ $$\text{and}$$ $$13x + 7 ≥ 12x + 13$$
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#4:
Instructions: Solve each inequality, write in interval notation, graph.
a) $$2(2 + 4n) < -12$$ $$\text{or}$$ $$9n + 19 > 46$$
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#5:
Instructions: Solve each inequality, write in interval notation, graph.
a) $$7 - 20v ≥ 67$$ $$\text{or}$$ $$8v + 9 ≥ -95$$
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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) $$\text{No Solution:} \: ∅$$
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#4:
Solutions:
a) $$n < -2 \: \text{or} \: n > 3$$
$$(-∞,-2) ∪ (3,∞)$$
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#5:
Solutions:
a) $$\text{All Real Numbers}$$
$$(-∞,∞)$$
