Question

solve the inequality - 2(w + 6)+8 < - 16. graph the solution. choose the correct graph below.

Explanation:

Step1: Simplify the left - hand side of the inequality

First, expand $-2(w + 6)+8$:
\[

$$\begin{align*} -2(w + 6)+8&=-2w-12 + 8\\ &=-2w-4 \end{align*}$$

\]
So the inequality becomes $-2w-4\lt - 16$.

Step2: Add 4 to both sides

Adding 4 to both sides of the inequality $-2w-4\lt - 16$ gives:
\[

$$\begin{align*} -2w-4 + 4&\lt - 16+4\\ -2w&\lt - 12 \end{align*}$$

\]

Step3: Divide both sides by - 2 and reverse the inequality sign

Dividing both sides of $-2w\lt - 12$ by - 2 (and reversing the inequality sign because we are dividing by a negative number) gives:
\[

$$\begin{align*} \frac{-2w}{-2}&>\frac{-12}{-2}\\ w&>6 \end{align*}$$

\]
On a number - line, we represent this as an open circle at 6 (because 6 is not included in the solution) and an arrow pointing to the right.

Answer:

The solution of the inequality is $w > 6$. The graph has an open circle at 6 and an arrow pointing to the right.