Question

graph your solution to the inequality. 2|(1/3)w + 1| - 13 < -5

Explanation:

Step1: Isolate the absolute - value expression

Add 13 to both sides of the inequality $2|\frac{1}{3}w + 1|-13\lt - 5$.
$2|\frac{1}{3}w + 1|\lt - 5 + 13$, so $2|\frac{1}{3}w + 1|\lt8$. Then divide both sides by 2: $|\frac{1}{3}w + 1|\lt4$.

Step2: Rewrite as a compound inequality

We know that if $|x|\lt a$ ($a\gt0$), then $-a\lt x\lt a$. So, $-4\lt\frac{1}{3}w + 1\lt4$.

Step3: Solve the left - hand side of the compound inequality

Subtract 1 from all parts: $-4-1\lt\frac{1}{3}w+1 - 1\lt4 - 1$, which gives $-5\lt\frac{1}{3}w\lt3$.

Step4: Solve for $w$

Multiply all parts by 3: $-5\times3\lt\frac{1}{3}w\times3\lt3\times3$, so $-15\lt w\lt9$.

Answer:

The solution on the number - line is an open interval from $-15$ to $9$. We use open circles at $-15$ and $9$ to indicate that these values are not included in the solution set.