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Question 1 of 5Solve for all solutions.
$$4\text{sec}\hspace{.1em}x + 2 < 3\text{sec}\hspace{.1em}x$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\frac{π}{2}+ 2πn < x < \frac{2π}{3}+ 2πn$$ $$\text{or}$$ $$\frac{4π}{3}+ 2πn < x < \frac{3π}{2}+ 2πn$$
B
$$\frac{2π}{3}+ 2πn < x < \frac{4π}{3}+ 2πn$$
C
$$\frac{2π}{3}+ 2πn < x < \frac{4π}{3}+ 2πn$$ $$\text{or}$$ $$\frac{3π}{2}+ 2πn < x < \frac{5π}{2}+ 2πn$$
D
$$\text{No Solution}$$
E
$$\frac{7π}{6}+ 2πn < x < \frac{11π}{6}+ 2πn$$
Question 2 of 5Solve for all solutions.
$$\text{tan}\hspace{.1em}x + \frac{-9 + \sqrt{3}}{3}> -3 $$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\frac{5π}{6}+ πn ≤ x ≤ \frac{3π}{2}+ πn$$
B
$$\frac{5π}{6}+ πn < x < \frac{3π}{2}+ πn$$
C
$$\text{No Solution}$$
D
$$\frac{π}{3}+ πn < x < \frac{π}{2}+ πn$$
E
$$\frac{π}{2}+ πn < x < \frac{5π}{6}+ πn$$
Question 3 of 5Solve for all solutions.
$$-8\text{cos}\left(x - \frac{4π}{3}\right) < -4\sqrt{3}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\text{No Solution}$$
B
$$\frac{3π}{2}+ 2πn < x < \frac{19π}{6}+ 2πn$$
C
$$\frac{7π}{6}+ 2πn < x < \frac{3π}{2}+ 2πn$$
D
$$\frac{π}{6}+ 2πn < x < \frac{5π}{6}+ 2πn$$
E
$$\frac{2π}{3}+ 2πn < x < \frac{4π}{3}+ 2πn$$
Question 4 of 5Solve for all solutions.
$$\sqrt{2}\text{sin}\hspace{.1em}x - 2\text{sin}\hspace{.1em}2x ≥ -3\text{sin}\hspace{.1em}2x$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\frac{π}{4}+ 2πn ≤ x ≤ \frac{3π}{4}+ 2πn$$
B
$$\text{No Solution}$$
C
$$\frac{3π}{4}+ 2πn ≤ x ≤ π + 2πn$$ $$\text{or}$$ $$\frac{5π}{4}+ 2πn ≤ x ≤ 2π + 2πn$$
D
$$2πn ≤ x ≤ \frac{3π}{4}+ 2πn$$ $$\text{or}$$ $$π + 2πn ≤ x ≤ \frac{5π}{4}+ 2πn$$
E
$$\frac{2π}{3}+ 2πn ≤ x ≤ \frac{4π}{3}+ 2πn$$
Question 5 of 5Solve for all solutions.
$$-2\text{cos}\hspace{.1em}x + 4\text{sin}\hspace{.1em}\frac{x}{2}< -3$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\frac{7π}{3}+ 4πn < x < \frac{11π}{3}+ 4πn$$
B
$$\frac{11π}{3}+ 4πn < x < \frac{19π}{3}+ 4πn$$
C
$$\frac{5π}{12}+ 4πn < x < \frac{19π}{12}+ 4πn$$
D
$$\text{No Solution}$$
E
$$\frac{π}{3}+ 4πn < x < \frac{2π}{3}+ 4πn$$ $$\text{or}$$ $$\frac{5π}{3}+ 4πn < x < \frac{11π}{6}+ 4πn$$

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