Question

solve the absolute - value inequality. graph the solution.
-2|x + 4|≤ - 6
graph the solution. choose the correct graph below.

Explanation:

Step1: Isolate absolute - value

Divide both sides by - 2 and reverse the inequality sign. We get $|x + 4|\geq3$.

Step2: Split into two inequalities

$x+4\geq3$ or $x + 4\leq - 3$.

Step3: Solve first inequality

$x+4\geq3$, subtract 4 from both sides: $x\geq - 1$.

Step4: Solve second inequality

$x + 4\leq - 3$, subtract 4 from both sides: $x\leq - 7$.

Answer:

The solution is $x\leq - 7$ or $x\geq - 1$. The correct graph is one with a closed - circle at $x=-7$ and shading to the left, and a closed - circle at $x = - 1$ and shading to the right. Without seeing the exact details of each graph, it should match this description.