Question

which number line represents the solution set for the inequality 2x - 6 > 6(x - 2) + 8? -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5

Explanation:

Step1: Expand the right - hand side

$2x - 6>6(x - 2)+8$ becomes $2x - 6>6x-12 + 8$.

Step2: Simplify the right - hand side

$2x - 6>6x - 4$.

Step3: Move terms with $x$ to one side

Subtract $2x$ from both sides: $-6>6x-2x - 4$, which is $-6>4x - 4$.

Step4: Move constant terms to one side

Add 4 to both sides: $-6 + 4>4x$, so $-2>4x$.

Step5: Solve for $x$

Divide both sides by 4: $x<-\frac{2}{4}=-\frac{1}{2}=-0.5$.
The solution set is all numbers less than $- 0.5$. The number line with an open - circle at $-0.5$ and an arrow pointing to the left represents this.

Answer:

The number line with an open - circle at $-0.5$ and an arrow pointing to the left.