Question

question
solve for ( x ) and graph the solution on the number line below.
( 17 > 3x + 2 geq -22 )
answer attempt 1 out of 2
< > ≤ ≥ or
inequality notation:
number line:
number line with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12 marked, arrows at both ends

Explanation:

Step1: Subtract 2 from all parts

To isolate the term with \(x\), we subtract 2 from each part of the compound inequality. So we have \(17 - 2>3x + 2- 2\geq - 22-2\), which simplifies to \(15>3x\geq - 24\).

Step2: Divide all parts by 3

To solve for \(x\), we divide each part of the inequality by 3. So \(\frac{15}{3}>\frac{3x}{3}\geq\frac{-24}{3}\), which simplifies to \(5 > x\geq - 8\) or in standard form \(-8\leq x < 5\).

Answer:

Inequality Notation: \(-8\leq x < 5\)

For the number line: We draw a closed circle at \(-8\) (because \(x\) is greater than or equal to \(-8\)) and an open circle at \(5\) (because \(x\) is less than \(5\)), then shade the region between \(-8\) and \(5\) on the number line.