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. ( 5x + 3 > -7 ) or ( 5x + 3 leq 48 ) answer inequality notation: number line:

Explanation:

Step1: Solve first inequality

Subtract 3 from both sides:
$5x + 3 - 3 > -7 - 3$
$5x > -10$
Divide by 5:
$\frac{5x}{5} > \frac{-10}{5}$
$x > -2$

Step2: Solve second inequality

Subtract 3 from both sides:
$5x + 3 - 3 \leq 48 - 3$
$5x \leq 45$
Divide by 5:
$\frac{5x}{5} \leq \frac{45}{5}$
$x \leq 9$

Step3: Combine solutions (OR)

The compound inequality uses "or", so we combine the two solution sets. Since $x > -2$ covers all values greater than -2, and $x \leq 9$ covers all values up to 9, together they include all real numbers.

Answer:

Inequality Notation: $\mathbb{R}$ (all real numbers)
Number Line: The entire number line is shaded (from negative infinity to positive infinity, with no gaps).