Question

1. graph the solution set to this inequality.

-(x + 4) - 2 > 2x + 6
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Explanation:

Step1: Simplify the left side

First, distribute the negative sign in \(-(x + 4)\) to get \(-x - 4\). Then subtract 2: \(-x - 4 - 2 = -x - 6\). So the inequality becomes \(-x - 6 > 2x + 6\).

Step2: Solve for \(x\)

Add \(x\) to both sides: \(-6 > 3x + 6\). Then subtract 6 from both sides: \(-12 > 3x\). Divide both sides by 3: \(-4 > x\) (or \(x < -4\)).

Step3: Graph the solution

On the number line, we have an open circle at \(-4\) (since \(x\) is not equal to \(-4\)) and an arrow pointing to the left (because \(x\) is less than \(-4\)).

Answer:

To graph the solution \(x < -4\), place an open circle at \(-4\) on the number line and draw an arrow to the left (towards more negative numbers).