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Question 1 of 5: Solve each inequality.
$$27^{x + 1}\cdot 27^{-2x + 3}≥ \frac{1}{9}$$
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A
$$x ≥ \frac{12}{5}$$ $$\left[\frac{12}{5}, \infty\right)$$ Graphing the interval on the number line
B
$$\text{No Solution}$$
C
$$x ≤ \frac{14}{3}$$ $$\left(-\infty, \frac{14}{3}\right]$$ Graphing the interval on the number line
D
$$x ≥ \frac{14}{3}$$ $$\left[\frac{14}{3}, \infty\right)$$ Graphing the interval on the number line
E
$$x ≥ -3$$ $$\left[-3, \infty\right)$$ Graphing the interval on the number line
Question 2 of 5: Solve each inequality.
$$\left(\frac{1}{9}\right)^x - \frac{28}{3^{x + 1}}< -3$$
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A
$$x < -2$$ $$\text{or}$$ $$x > 1$$ $$\left(-\infty, -2\right) ∪ \left(1, \infty\right)$$ Graphing the interval on the number line
B
$$-2 < x < 1$$ $$(-2, 1)$$ Graphing the interval on the number line
C
$$-2 < x < 8$$ $$(-2, 8)$$ Graphing the interval on the number line
D
$$\text{No Solution}$$
E
$$x < -8$$ $$\text{or}$$ $$x > 2$$ $$\left(-\infty, -8\right) ∪ \left(2, \infty\right)$$ Graphing the interval on the number line
Question 3 of 5: Solve each inequality.
$$\log(x + 23) + \log(x + 8) ≤ 2$$
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A
$$-8 < x ≤ -3$$ $$(-8, -3]$$ Graphing the interval on the number line
B
$$x ≥ -3$$ $$[-3, \infty)$$ Graphing the interval on the number line
C
$$\text{No Solution}$$
D
$$x ≤ -8$$ $$(-\infty, -8]$$ Graphing the interval on the number line
E
$$3 ≤ x ≤ 8$$ $$[3, 8]$$ Graphing the interval on the number line
Question 4 of 5: Solve each inequality.
$$\log^2(x) + \log(x) ≥ 6$$
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A
$$\text{No Solution}$$
B
$$x ≥ 100$$ $$[100, \infty)$$ Graphing the interval on the number line
C
$$0 < x ≤ 100$$ $$(0, 100]$$ Graphing the interval on the number line
D
$$0 < x ≤ \frac{1}{1{,}000}$$ $$\left(0, \frac{1}{1{,}000}\right]$$ Graphing the interval on the number line
E
$$0 < x ≤ \frac{1}{1{,}000}$$ $$\text{or}$$ $$x ≥ 100$$ $$\left(0, \frac{1}{1{,}000}\right] ∪ [100, \infty)$$ Graphing the interval on the number line
Question 5 of 5: Solve each inequality.
$$\log_9(x + 5) ≤ \log_5(x + 5)$$
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A
$$x > -5$$ $$(-5, \infty)$$ Graphing the interval on the number line
B
$$-5 < x ≤ -4$$ $$(-5, -4]$$ Graphing the interval on the number line
C
$$\text{No Solution}$$
D
$$x ≥ -4$$ $$[-4, \infty)$$ Graphing the interval on the number line
E
$$-5 < x ≤ 0$$ $$\text{or}$$ $$x ≥ 4$$ $$(-5, 0] ∪ [4, \infty)$$ Graphing the interval on the number line

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