Question

solve for x and graph the solution on the number line below.

$-7 \leq 2x + 7 \leq 31$

answer attempt 1 out of 5

inequality notation:

number line:

Explanation:

Step1: Subtract 7 from all parts

To isolate the term with \(x\), we subtract 7 from each part of the compound inequality. So we have \(-7 - 7\leq2x + 7-7\leq31 - 7\), which simplifies to \(-14\leq2x\leq24\).

Step2: Divide all parts by 2

To solve for \(x\), we divide each part of the inequality by 2. That gives \(\frac{-14}{2}\leq\frac{2x}{2}\leq\frac{24}{2}\), which simplifies to \(-7\leq x\leq12\).

Answer:

Inequality Notation: \(-7\leq x\leq12\)
For the number line: We mark a closed circle at \(-7\) and \(12\) (since the inequality is "less than or equal to" and "greater than or equal to") and shade the region between \(-7\) and \(12\) on the number line.