If $$-22 < 13 - 5q < 8$$, what is the minimum possible integer value of $$q$$?

Correct.
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First, isolate the variable as in one-variable linear equations. In this case, subtract $$13$$ from each part of the inequality.
>$$-22-13 < 13 - 5q-13 < 8-13$$
>$$-35 < -5q < -5$$
Divide each part of the inequality by $$-5$$ and flip the signs of the inequalities.
>$$\displaystyle \frac{-35}{-5} > \frac{-5q}{-5} > \frac{-5}{-5}$$
>$$7 > q > 1$$
The minimum integer value of $$q$$ is $$2$$ because $$q$$ must be greater than $$1$$. Hence, this is the correct answer.

Incorrect.
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Carefully check your calculations.

Incorrect.
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Carefully check your work. Note that the inequality symbols are *strict* inequality symbols, not ≤ or ≥.

Incorrect.
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You might have gotten this answer if you found the *maximum* possible integer value of $$q$$.

Incorrect.
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Carefully check your answer. Make sure you find the *minimum* possible integer value of $$q$$.

$$7$$

$$6$$

$$2$$

$$1$$

$$-1$$