Question

solve the inequality. graph the solution set and write it in interval not - 4(x - 2)-2x < -(4x + 4)+2x. choose the correct graph below. a. graph with arrow starting from 0 and ending at 3. b. graph not fully shown. c. graph with arrow starting from 0 and ending at 3 with a closed - end at 3. d. graph not fully shown. write the answer in interval notation.

Explanation:

Step1: Expand both sides

Expand $-4(x - 2)-2x$ to $-4x + 8-2x=-6x + 8$, and expand $-(4x + 4)+2x=-4x-4 + 2x=-2x-4$. So the inequality becomes $-6x + 8<-2x-4$.

Step2: Move x - terms to one side

Add $6x$ to both sides: $8<-2x-4 + 6x$, which simplifies to $8<4x-4$.

Step3: Isolate the x - term

Add 4 to both sides: $8 + 4<4x$, so $12<4x$.

Step4: Solve for x

Divide both sides by 4: $x > 3$.

The graph of the solution set has an open - circle at 3 and a ray pointing to the right.

Answer:

The correct graph is the one with an open - circle at 3 and a ray pointing to the right (not shown in the options provided completely, but conceptually). In interval notation, the solution is $(3,\infty)$.