Question

solve for x and graph the solution on the number line below. -32 < -3x + 4 ≤ 16 answer attempt 1 out of 2 < > ≤ ≥ or inequality notation: number line: -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Explanation:

Step1: Subtract 4 from all parts

Subtract 4 from each part of the compound - inequality:
\(-32 - 4\lt - 3x+4 - 4\leqslant16 - 4\)
\(-36\lt - 3x\leqslant12\)

Step2: Divide all parts by - 3 and reverse the inequality signs

When dividing an inequality by a negative number, the direction of the inequality signs changes.
\(\frac{-36}{-3}\gt\frac{-3x}{-3}\geqslant\frac{12}{-3}\)
\(12\gt x\geqslant - 4\)

Answer:

Inequality Notation: \(-4\leqslant x\lt12\)
Number - Line: Mark a closed circle at \(-4\) (because \(x\) can equal \(-4\)) and an open circle at \(12\) (because \(x\) cannot equal \(12\)), and shade the region between them.