Question

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 (∅), leave the number line blank. 5x + 4 > -11 and 34 ≤ 5x + 4 answer inequality notation: number line: touch and drag to plot them. submit answer

Explanation:

Step1: Solve first inequality

Subtract 4 from both sides:
$5x + 4 - 4 > -11 - 4$
$5x > -15$
Divide by 5:
$\frac{5x}{5} > \frac{-15}{5}$
$x > -3$

Step2: Solve second inequality

Subtract 4 from both sides:
$34 - 4 \leq 5x + 4 - 4$
$30 \leq 5x$
Divide by 5:
$\frac{30}{5} \leq \frac{5x}{5}$
$6 \leq x$
Rewrite as $x \geq 6$

Step3: Combine with "and"

The compound inequality requires both conditions to be true. Since $x \geq 6$ is a stricter condition than $x > -3$, the combined solution is the overlap of the two sets.

Answer:

Inequality Notation: $x \geq 6$

For the number line: Plot a closed circle at 6, and draw a line extending to the right (towards positive infinity).