Question

solve the inequality. graph the solution set and write it in interval notation. -6(x - 3)-2x<-(3x + 10)+2x
choose the correct graph below.
a.
c.

Explanation:

Step1: Expand both sides

First, expand the expressions:
-6(x - 3)-2x=-6x + 18-2x=-8x + 18, and -(3x + 10)+2x=-3x-10 + 2x=-x-10.
The inequality becomes -8x + 18 < -x-10.

Step2: Move x - terms to one side

Add 8x to both sides:
-8x+8x + 18 < -x+8x-10, which simplifies to 18 < 7x-10.

Step3: Isolate x

Add 10 to both sides:
18 + 10 < 7x-10 + 10, so 28 < 7x.
Then divide both sides by 7:
\frac{28}{7}<\frac{7x}{7}, resulting in 4 < x or x>4.

Step4: Graph and interval - notation

The solution in interval notation is (4,+\infty). The graph has an open - circle at 4 and a ray extending to the right.

Answer:

The solution set in interval notation is (4,+\infty). The correct graph is not shown completely in the provided options, but it should have an open - circle at 4 and a ray extending to the right.