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Question 1 of 5Solve each inequality.
$$x^3 + 2x^2 < 4x + 8$$
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A
$$x < -2$$ $$\text{or}$$ $$-2 < x < 2$$ $$(-∞, -2) ∪ (-2, 2)$$ Graphing the interval on the number line
B
$$x > 2$$ $$(2, ∞)$$ Graphing the interval on the number line
C
$$x < 2$$ $$(-∞, 2)$$ Graphing the interval on the number line
D
$$-2 < x < 2$$ $$(-2, 2)$$ Graphing the interval on the number line
E
$$x < -2$$ $$(-∞, -2)$$ Graphing the interval on the number line
Question 2 of 5Solve each inequality.
$$12x^3 ≥ 30x^2 -2x + 5$$
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A
$$x ≤ \frac{5}{2}$$ $$\left(-∞, \frac{5}{2}\right]$$ Graphing the interval on the number line
B
$$x ≥ \frac{5}{2}$$ $$\left[\frac{5}{2}, ∞\right)$$ Graphing the interval on the number line
C
$$x ≤ 0$$ $$\text{or}$$ $$x ≥ \frac{5}{2}$$ $$(-∞, 0] ∪ \left[\frac{5}{2}, ∞\right)$$ Graphing the interval on the number line
D
$$-\frac{5}{2} ≤ x ≤ \frac{5}{2}$$ $$\left[-\frac{5}{2}, \frac{5}{2}\right]$$ Graphing the interval on the number line
E
$$0 ≤ x ≤ \frac{5}{2}$$ $$\left[0, \frac{5}{2}\right]$$ Graphing the interval on the number line
Question 3 of 5Solve each inequality.
$$\left(x - \frac{1}{2}\right)^2(x - 5)^2(x - 2) > 0$$
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A
$$x < 2$$ $$(-∞, 2)$$ Graphing the interval on the number line
B
$$x < \frac{1}{2}$$ $$\left(-∞, \frac{1}{2}\right)$$ Graphing the interval on the number line
C
$$x < \frac{1}{2}$$ $$\text{or}$$ $$\frac{1}{2} < x < 2$$ $$\left(-∞, \frac{1}{2}\right) ∪ \left(\frac{1}{2}, 2\right)$$ Graphing the interval on the number line
D
$$2 < x < 5$$ $$\text{or}$$ $$x > 5$$ $$(2, 5) ∪ (5, ∞)$$ Graphing the interval on the number line
E
$$x > 5$$ $$(5, ∞)$$ Graphing the interval on the number line
Question 4 of 5Solve each inequality.
$$\left(x - \frac{3}{2}\right)^3(x - 4)^2(x + 1) > 0$$
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A
$$x < -1$$ $$(-∞, -1)$$ Graphing the interval on the number line
B
$$x < -1$$ $$\text{or}$$ $$\frac{3}{2} < x < 4$$ $$\text{or}$$ $$x > 4$$ $$(-∞, -1) ∪ \left(\frac{3}{2}, 4\right) ∪ (4, ∞)$$ Graphing the interval on the number line
C
$$x > 4$$ $$(4, ∞)$$ Graphing the interval on the number line
D
$$-1 < x < 4$$ $$(-1, 4)$$ Graphing the interval on the number line
E
$$x < 4$$ $$(-∞, 4)$$ Graphing the interval on the number line
Question 5 of 5Solve each inequality.
$$x\left(x - \frac{3}{2}\right)^2 \left(x + \frac{1}{2}\right)^2(2x - 5) < 0$$
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A
No Solution
B
All Real Numbers $$(-∞, ∞)$$ Graphing the interval on the number line
C
$$0 < x < \frac{3}{2}$$ $$\text{or}$$ $$\frac{3}{2} < x < \frac{5}{2}$$ $$\left(0, \frac{3}{2}\right) ∪ \left(\frac{3}{2}, \frac{5}{2}\right)$$ Graphing the interval on the number line
D
$$x < -\frac{1}{2}$$ $$\text{or}$$ $$-\frac{1}{2} < x < 0$$ $$\text{or}$$ $$x > \frac{5}{2}$$ $$\left(-∞, -\frac{1}{2}\right) ∪ \left(-\frac{1}{2}, 0\right) ∪ \left(\frac{5}{2}, ∞\right)$$ Graphing the interval on the number line
E
$$-\frac{1}{2} < x < \frac{5}{2}$$ $$\left(-\frac{1}{2}, \frac{5}{2}\right)$$ Graphing the interval on the number line

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