Question

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

$-31>5x + 9\geq-41$

answer attempt 1 out of 3

$<$$>$$\leq$$\geq$or

inequality notation:

number line:

submit answer

Explanation:

Step1: Subtract 9 from all parts

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

Step2: 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: $-10\leq x < - 8$

For graphing on the number - line:

• Put a closed circle at $x = - 10$ (because the inequality includes equality for $x=-10$: $x\geq - 10$)
• Put an open circle at $x=-8$ (because the inequality is strict for $x < - 8$)
• Draw a line segment connecting the two points.