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.
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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.
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Simplify both inequalities and solve for $$x$$.
$$32< x<39$$
$$32>x>-39$$
$$39>x>-32$$
$$x>-39$$
$$x<32$$
