Question

what value of x is in the solution set of the inequality -2(3x + 2) > -8x + 6?
-6
-5
5
6

Explanation:

Step1: Expand the left side

First, we expand \(-2(3x + 2)\) using the distributive property \(a(b + c)=ab+ac\). So, \(-2(3x + 2)=-6x-4\). The inequality becomes \(-6x - 4>-8x + 6\).

Step2: Add \(8x\) to both sides

To get all the \(x\) terms on one side, we add \(8x\) to both sides of the inequality. \(-6x+8x - 4>-8x + 8x+ 6\), which simplifies to \(2x-4>6\).

Step3: Add 4 to both sides

Next, we add 4 to both sides to isolate the term with \(x\). \(2x-4 + 4>6 + 4\), so \(2x>10\).

Step4: Divide by 2

Then, we divide both sides by 2 to solve for \(x\). \(\frac{2x}{2}>\frac{10}{2}\), which gives \(x > 5\).

Now we check the options:

• For \(x=-6\): \(-6

ot>5\), so not in the solution set.

• For \(x=-5\): \(-5

ot>5\), so not in the solution set.

• For \(x = 5\): \(5

ot>5\) (it's equal), so not in the solution set.

• For \(x=6\): \(6>5\), so it is in the solution set.

Answer:

D. 6