Question

solve for x and graph the solution on the number line below. 4x + 7 ≥ -13 and 15 ≥ 4x + 7 answer attempt 1 out of 2 < > ≤ ≥ or inequality notation: number line: -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 click and drag to plot line.

Explanation:

Step1: Solve the first inequality

Subtract 7 from both sides of $4x + 7\geq - 13$.
$4x+7 - 7\geq - 13 - 7$, which simplifies to $4x\geq - 20$. Then divide both sides by 4: $x\geq - 5$.

Step2: Solve the second inequality

Subtract 7 from both sides of $15\geq4x + 7$.
$15 - 7\geq4x+7 - 7$, which simplifies to $8\geq4x$. Then divide both sides by 4: $2\geq x$ or $x\leq2$.

Step3: Find the intersection

We need to find the values of $x$ that satisfy both $x\geq - 5$ and $x\leq2$. So, $-5\leq x\leq2$.

Answer:

Inequality Notation: $-5\leq x\leq2$
Number - Line: Plot a closed - circle at $x=-5$ and a closed - circle at $x = 2$, and shade the region between them.