Question

solve the inequality. graph the solution. - 2(w + 6)+8 < - 18. choose the correct graph below.

Explanation:

Step1: Simplify the left - hand side

First, expand $-2(w + 6)$ using the distributive property $a(b + c)=ab+ac$. Here $a=-2$, $b = w$, $c = 6$. So $-2(w + 6)=-2w-12$. The inequality becomes $-2w-12+8\lt - 18$.
Combine like - terms: $-2w-4\lt - 18$.

Step2: Isolate the variable term

Add 4 to both sides of the inequality. According to the addition property of inequalities, if $a\lt b$, then $a + c\lt b + c$. So $-2w-4 + 4\lt - 18+4$, which simplifies to $-2w\lt - 14$.

Step3: Solve for w

Divide both sides of the inequality by - 2. When dividing an inequality by a negative number, the direction of the inequality sign changes. According to the division property of inequalities, if $a\lt b$ and $c\lt0$, then $\frac{a}{c}\gt\frac{b}{c}$. So $\frac{-2w}{-2}\gt\frac{-14}{-2}$, which gives $w\gt7$.

The solution of the inequality $w\gt7$ is all real numbers greater than 7. On a number line, this is represented by an open circle at 7 (because 7 is not included in the solution) and an arrow pointing to the right.

Answer:

D. (assuming option D is the number - line with an open circle at 7 and an arrow pointing to the right)