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# Inequalities: Overview

If $$-17 ≤ 3 - 4q ≤ 47$$, what is the difference between the maximum and minimum possible values of $$q ~ ?$$
Correct. [[Snippet]] First, isolate the variable as in one-variable linear equations. In this case, subtract $$3$$ from each part of the inequality. >$$-17 -3 ≤ 3 - 4q -3 ≤ 47 - 3$$ >$$-20 ≤ -4q ≤ 44$$ Divide each part of the inequality by $$-4$$ and {color:red}flip{/color} the inequalities. >$$\frac{-20}{-4} ≥ \frac{-4q}{-4} ≥ \frac{44}{-4}$$ >$$5 ≥ q ≥ -11$$ To find the difference between the maximum and minimum possible values, subtract $$-11$$ from $$5$$. >$$5 - (-11) = 5 + 11 = 16$$ Hence, this is the correct answer.

Incorrect.

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Incorrect.

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Incorrect.

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Incorrect.

[[Snippet]] Did you use $$11 - 5 = 6$$ (or $$5 - 11 = -6$$) when calculating the difference? Remember that minus times minus is plus, and the minus signs cancel each other out.
$$5$$
$$6$$
$$11$$
$$15$$
$$16$$