Question

solve for x and graph the solution on the number line below.
-32 < -3x + 4 ≤ 16
answer
< > ≤ ≥ or
inequality notation:
number line:
< -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 >
click and drag to plot line.
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Explanation:

Step1: Subtract 4 from all parts

Subtract 4 from each part of the compound - inequality $-32 < - 3x + 4\leq16$.
$-32-4 < -3x + 4 - 4\leq16 - 4$
$-36 < -3x\leq12$

Step2: Divide all parts by - 3

When dividing an inequality by a negative number, the direction of the inequality signs changes.
$\frac{-36}{-3}>\frac{-3x}{-3}\geq\frac{12}{-3}$
$12 > x\geq - 4$

Answer:

Inequality Notation: $-4\leq x<12$
To graph on the number - line:

• Place a closed circle at $x = - 4$ (because $x$ can equal $-4$) and an open circle at $x = 12$ (because $x$ cannot equal $12$).
• Draw a line segment connecting the two points.