Question

solve the linear inequality and graph the solution.
8 > 2 - 2x - 4
x > -5
x < -5
x ≥ -5
x ≤ -5

Explanation:

Step1: Simplify the right - hand side

First, simplify $2−2x - 4$ to $-2 - 2x$. So the inequality becomes $8>-2 - 2x$.

Step2: Add 2 to both sides

Adding 2 to both sides gives $8 + 2>-2-2x+2$, which simplifies to $10>-2x$.

Step3: Divide both sides by - 2

When dividing both sides of the inequality $10>-2x$ by - 2, we need to reverse the inequality sign. So we get $\frac{10}{-2}<\frac{-2x}{-2}$, which simplifies to $-5 < x$ or $x>-5$.

Step4: Graph the solution

The solution $x > - 5$ is graphed as an open - circle at $x=-5$ (because $x$ is strictly greater than - 5) and an arrow pointing to the right.

Answer:

A. $x > - 5$ (the first option with an open - circle at - 5 and arrow pointing to the right)