Question

solve for x and graph the solution on the number line below. -32 < -3x + 4 ≤ 16 answer attempt 1 out of 2 inequality notation: number line:

Explanation:

Step1: Subtract 4 from all parts

To isolate the term with \(x\), we subtract 4 from each part of the compound inequality.
\[
-32 - 4 < -3x + 4 - 4 \leq 16 - 4
\]
\[
-36 < -3x \leq 12
\]

Step2: Divide by -3 (reverse inequalities)

When dividing by a negative number, the direction of the inequality signs reverses.
\[
\frac{-36}{-3} > \frac{-3x}{-3} \geq \frac{12}{-3}
\]
\[
12 > x \geq -4
\]
Which can be rewritten as \(-4 \leq x < 12\)

Answer:

Inequality Notation: \(-4 \leq x < 12\)
(For the number line: Draw a closed circle at -4, an open circle at 12, and shade the region between them.)