Question

solve for ( x ) and graph the solution on the number line below. if possible, resolve your answer to a single inequality. in case of no solution (( varnothing )), leave the number line blank. (-37 < 5x + 3) or ( 5x + 3 leq 23)
answer
inequality notation:
number line:

Explanation:

Step1: Solve first inequality

Subtract 3 from both sides:
$-37 - 3 < 5x + 3 - 3$
$-40 < 5x$
Divide by 5:
$\frac{-40}{5} < \frac{5x}{5}$
$x > -8$

Step2: Solve second inequality

Subtract 3 from both sides:
$5x + 3 - 3 \leq 23 - 3$
$5x \leq 20$
Divide by 5:
$\frac{5x}{5} \leq \frac{20}{5}$
$x \leq 4$

Step3: Combine solutions

The compound inequality uses "or", so combine the two results.

Answer:

Inequality Notation:

$x > -8$ or $x \leq 4$

Number Line:

• Draw an open circle at $-8$ and shade all values to the right.
• Draw a closed circle at $4$ and shade all values to the left.

(This covers all real numbers, so the entire number line is shaded.)