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.
0
c.
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Explanation:

Step1: Expand both sides

Expand -6(x - 3) to -6x+18 and -(3x + 10) to -3x - 10. The inequality becomes -6x + 18-2x<-3x - 10+2x.

Step2: Combine like - terms

On the left - hand side, -6x-2x=-8x, so it's -8x + 18. On the right - hand side, -3x+2x=-x, so it's -x - 10. The inequality is now -8x + 18<-x - 10.

Step3: Add 8x to both sides

We get 18<-x - 10+8x, which simplifies to 18<7x - 10.

Step4: Add 10 to both sides

18 + 10<7x, so 28<7x.

Step5: Divide both sides by 7

We have 4<x, or x > 4.
The solution set in interval notation is (4, +∞). The graph of the solution set is a number line with an open circle at 4 and a ray pointing to the right.

Answer:

The correct graph is one with an open circle at 4 and a ray pointing to the right. Since the options are not fully shown, but based on the solution x>4, if there is an option with an open circle at 4 and a right - pointing ray, that is the correct one.