Question

solve for $x$ and graph the solution on the number line below.$-31 > 5x + 9 \geq -41$answer attempt 1 out of 2$<$ $>$ $leq$ $geq$ orinequality notation:number 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

$\frac{-40}{5} > \frac{5x}{5} \geq \frac{-50}{5}$
$-8 > x \geq -10$
This can also be rewritten as $-10 \leq x < -8$

Answer:

Inequality Notation: $\boldsymbol{-10 \leq x < -8}$

For the number line:

1. Place a closed (filled) circle at $x=-10$ (since the inequality includes equality $\geq$)
2. Place an open (unfilled) circle at $x=-8$ (since the inequality is strict $<$)
3. Draw a solid line connecting the two circles to represent all values between $-10$ and $-8$.