Question

solve for x and graph the solution on the number line below. -31 > 5x + 9 ≥ -41 answer attempt 1 out of 2 < > ≤ ≥ or inequality notation: number line:

Explanation:

Step1: Isolate the variable - subtract 9 from all parts

\[

$$\begin{align*} -31-9&>5x + 9-9\geq - 41-9\\ -40&>5x\geq -50 \end{align*}$$

\]

Step2: Solve for x - divide all parts by 5

\[

$$\begin{align*} \frac{-40}{5}&>\frac{5x}{5}\geq\frac{-50}{5}\\ - 8&>x\geq - 10 \end{align*}$$

\]

Answer:

Inequality Notation: $-10\leq x < - 8$
Number Line: Mark a closed - circle at $-10$ (because $x$ can equal $-10$), an open - circle at $-8$ (because $x$ cannot equal $-8$), and shade the region between them.