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. (-13 geq 3x + 5) and ( 14 geq 3x + 5)
answer attempt 1 out of 2
inequality notation:
number line:

Explanation:

Step1: Solve first inequality

Subtract 5 from both sides:
$-13 - 5 \geq 3x + 5 - 5$
$-18 \geq 3x$
Divide by 3:
$\frac{-18}{3} \geq \frac{3x}{3}$
$x \leq -6$

Step2: Solve second inequality

Subtract 5 from both sides:
$14 - 5 \geq 3x + 5 - 5$
$9 \geq 3x$
Divide by 3:
$\frac{9}{3} \geq \frac{3x}{3}$
$x \leq 3$

Step3: Find intersection of solutions

Since we need values of $x$ that satisfy both inequalities, we take the stricter condition.

Answer:

Inequality Notation: $x \leq -6$

Number Line:

Draw a closed circle at $-6$ on the number line, and shade all values to the left of $-6$ (including $-6$).