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 in interval notation, graph.
$$a)$$ $$1 - 9x > 1 + 7x$$ $$\text{and}$$ $$x + 1 ≥ -6 - 6x$$
$$b)$$ $$9x + 10 > 10 + 8x$$ $$\text{and}$$ $$5x + 5 ≥ 8x - 1$$
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#2:
Instructions: solve each inequality, write in interval notation, graph.
$$a)$$ $$9x + 8 > 7x - 6$$ $$\text{and}$$ $$6x - 1 > 7x - 10$$
$$b)$$ $$7x - 8 < 8 + 6x$$ $$\text{and}$$ $$7 + x ≤ 3x + 9$$
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#3:
Instructions: solve each inequality, write in interval notation, graph.
$$a)$$ $$4 + 6x > 4 + x$$ $$\text{and}$$ $$-8 + 5x > 5x - 10$$
$$b)$$ $$8x + 1 < 7x - 2$$ $$\text{or}$$ $$-x - 8 < 2 + 4x$$
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#4:
Instructions: solve each inequality, write in interval notation, graph.
$$a)$$ $$5x + 6 > 4x + 6$$ $$\text{or}$$ $$5x - 2 ≥ x - 10$$
$$b)$$ $$5x - 8 > 7 + 2x$$ $$\text{or}$$ $$-9x - 9 > -9 + 9x$$
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#5:
Instructions: solve each inequality, write in interval notation, graph.
$$a)$$ $$-2x -\frac{4}{3}≥ 2x + \frac{3}{2}$$ $$\text{or}$$ $$\frac{5}{2}x - \frac{7}{2}> -2x + \frac{1}{2}$$
$$b)$$ $$1.6 - 1.6x < 2.3 - 1.2x$$ $$\text{or}$$ $$2.9x + 2.6 ≥ 3x - 0.2$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}{-}1 ≤ x < 0, [-1,0)$$
$$b)\hspace{.2em}0 < x ≤ 2, (0,2]$$
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#2:
Solutions:
$$a)\hspace{.2em}{-}7 < x < 9, (-7,9)$$
$$b)\hspace{.2em}{-}1 ≤ x < 16, [-1,16)$$
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#3:
Solutions:
$$a)\hspace{.2em}x > 0, (0, \infty)$$
$$b)\hspace{.2em}x < -3 \hspace{.2em}\text{or}\hspace{.2em}x > -2$$ $$(-\infty, -3) ∪ (-2, \infty)$$
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#4:
Solutions:
$$a)\hspace{.2em}x ≥ -2, [-2,\infty)$$
$$b)\hspace{.2em}x < 0 \hspace{.2em}\text{or}\hspace{.2em}x > 5$$ $$(-\infty, 0) ∪ (5,\infty)$$
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#5:
Solutions:
$$a)\hspace{.2em}x ≤ -\frac{17}{24}\hspace{.2em}\text{or}\hspace{.2em}x > \frac{8}{9}$$ $$\left(-\infty, -\frac{17}{24}\right] ∪ \left(\frac{8}{9}, \infty\right)$$
$$b)\hspace{.2em}\text{All Real Numbers}$$ $$(-\infty, \infty)$$
