### 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.

$$a)$$ $$1 - 9x > 1 + 7x$$ $$and$$ $$x + 1 ≥ -6 - 6x$$

$$b)$$ $$9x + 10 > 10 + 8x$$ $$and$$ $$5x + 5 ≥ 8x - 1$$

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#2:

Instructions: solve each inequality, write in interval notation, graph.

$$a)$$ $$9x + 8 > 7x - 6$$ $$and$$ $$6x - 1 > 7x - 10$$

$$b)$$ $$7x - 8 < 8 + 6x$$ $$and$$ $$7 + x ≤ 3x + 9$$

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#3:

Instructions: solve each inequality, write in interval notation, graph.

$$a)$$ $$4 + 6x > 4 + x$$ $$and$$ $$-8 + 5x > 5x - 10$$

$$b)$$ $$8x + 1 < 7x - 2$$ $$or$$ $$-x - 8 < 2 + 4x$$

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#4:

Instructions: solve each inequality, write in interval notation, graph.

$$a)$$ $$5x + 6 > 4x + 6$$ $$or$$ $$5x - 2 ≥ x - 10$$

$$b)$$ $$5x - 8 > 7 + 2x$$ $$or$$ $$-9x - 9 > -9 + 9x$$

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#5:

Instructions: solve each inequality, write in interval notation, graph.

$$a)$$ $$-2x -\frac{4}{3}≥ 2x + \frac{3}{2}$$ $$or$$ $$\frac{5}{2}x - \frac{7}{2}> -2x + \frac{1}{2}$$

$$b)$$ $$1.6 - 1.6x < 2.3 - 1.2x$$ $$and$$ $$2.9x + 2.6 ≥ 3x - 0.2$$

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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:

$$a)\hspace{.2em}(-\infty, \infty)$$

$$b)\hspace{.2em}x < -3 \hspace{.2em}or \hspace{.2em}x > -2$$ $$(-\infty, -3) ∪ (-2, \infty)$$

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#4:

Solutions:

$$a)\hspace{.2em}x ≥ -2, [-2,\infty)$$

$$b)\hspace{.2em}x < 0 \hspace{.2em}or \hspace{.2em}x > 5$$ $$(-\infty, 0) ∪ (5,\infty)$$

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#5:

Solutions:

$$a)\hspace{.2em}x ≤ -\frac{17}{24}\hspace{.2em}or \hspace{.2em}x > \frac{8}{9}$$ $$\left(-\infty, -\frac{17}{24}\right] ∪ \left(\frac{8}{9}, \infty\right)$$

$$b)\hspace{.2em}-1.75 < x ≤ 28, (-1.75, 28]$$