# Inequalities: Overview

If $$-17 ≤ 3 - 4q ≤ 47$$, what is the difference between the maximum and minimum possible values of $$q ~ ?$$

Correct.
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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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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.

$$5$$

$$6$$

$$11$$

$$15$$

$$16$$