Question

solve for $x$ and graph the solution on the number line below.
$-31 > 5x + 9 \geq -41$
answer attempt 2 out of 2
$<$, $>$, $\leq$, $\geq$, or
inequality notation: $-10 \leq x < -8$
number line:
click and drag to plot line.

Explanation:

Step1: Subtract 9 from all parts

$$-31 - 9 > 5x + 9 - 9 \geq -41 - 9$$
$$-40 > 5x \geq -50$$

Step2: Divide all parts by 5

$$\frac{-40}{5} > \frac{5x}{5} \geq \frac{-50}{5}$$
$$-8 > x \geq -10$$
(rewritten for standard notation: $-10 \leq x < -8$)

Step3: Graph on number line

• Place a closed circle at $x=-10$ (since $\geq$ includes the value)
• Place an open circle at $x=-8$ (since $<$ does not include the value)
• Draw a line segment connecting the two circles to show all values between them.

Answer:

Inequality Notation: $\boldsymbol{-10 \leq x < -8}$
Number Line: A closed dot at $-10$, an open dot at $-8$, and a solid line segment connecting the two points.