How do you solve $-4<=-3x - 7<5$ ?

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Answer 1 · 2018-04-04T12:25:27

$-4 < x <= -1$

If the expressions were more complex, we would have split the statement into two inequalities and solved them separately.

We will work with all three expressions at the same time.

Add 7 to each expression

$-4 color(blue)(+7) <= -3x-7 color(blue)(+7) < 5 color(blue)(+7)$

$3 <= color(red)(-3)x <12$

We will divide each term by $-3$ , but this causes the inequality signs to change.

$3/color(red)(-3) >= (color(red)(-3)x)/(color(red)(-3)) > 12/color(red)(-3)$

$-1 " ">=x" " > -4$

Or

$-4 < x <= -1$

How do you solve -4<=-3x - 7<5-4<=-3x - 7<5?