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Inequalities: Inequalities Involving an Absolute Value - The Number Case

If $$|2x + 7| < 71$$, which of the following inequalities gives the possible values of $$x$$?
Correct. Solve absolute values of the number case by considering two possible scenarios. First scenario: Copy the inequality without the absolute value brackets and solve. >$$2x + 7 < 71$$ >$$2x < 71 - 7$$ >$$2x < 64$$ Divide both sides by 2 to isolate $$x$$. >$$x < \frac{64}{2}$$ >$$x < 32$$ Second scenario: Remove the absolute value brackets. Put a negative sign around the other side of the inequality, AND flip the sign. >$$2x + 7 > -71$$ >$$2x > -71 - 7$$ >$$2x > -78$$ Divide both sides by 2 to isolate $$x$$. >$$x > -\frac{78}{2}$$ >$$x > -39$$ Finally, combine the two scenarios into one range for $$x$$, to get >$$32 > x > -39$$. Hence, this is the correct answer.
Incorrect. [[snippet]] Carefully check your work.

Incorrect.

[[Snippet]]

This answer choice is only partially true. While $$x$$ is less than 32, it must be greater than -39, too. Hence, this is not the correct answer.

Incorrect.

[[Snippet]]

This answer choice is only partially true. While $$x$$ is greater than -39, it must be less than 32, too. Hence, this is not the correct answer.
Incorrect. [[snippet]] Simplify both inequalities and solve for $$x$$.
$$32< x<39$$
$$32>x>-39$$
$$39>x>-32$$
$$x>-39$$
$$x<32$$