Question

what value of x is in the solution set of the inequality $8x - 6 > 12 + 2x$?

• $-1$
• $0$
• $3$
• $5$

Explanation:

Step1: Subtract \(2x\) from both sides

To simplify the inequality \(8x - 6>12 + 2x\), we subtract \(2x\) from each side. This gives us \(8x-2x - 6>12+2x - 2x\), which simplifies to \(6x-6 > 12\).

Step2: Add 6 to both sides

Next, we add 6 to both sides of the inequality \(6x - 6>12\). So, \(6x-6 + 6>12 + 6\), which simplifies to \(6x>18\).

Step3: Divide by 6

Then, we divide both sides of the inequality \(6x>18\) by 6. This gives us \(\frac{6x}{6}>\frac{18}{6}\), so \(x > 3\).

Now we check the options:

• For \(x=-1\): \(-1

ot>3\), so it's not in the solution set.

• For \(x = 0\): \(0

ot>3\), so it's not in the solution set.

• For \(x=3\): \(3

ot>3\) (since the inequality is \(x>3\)), so it's not in the solution set.

• For \(x = 5\): \(5>3\), so it is in the solution set.

Answer:

D. 5 (assuming the options are labeled A: -1, B: 0, C: 3, D: 5)