Question

what value of x is in the solution set of the inequality $4x - 12 \leq 16 + 8x$?
-10
-9
-8
-7

Explanation:

Step1: Subtract \(4x\) from both sides

To simplify the inequality \(4x - 12 \leq 16 + 8x\), we first subtract \(4x\) from each side. This gives us \(-12 \leq 16 + 4x\).

Step2: Subtract 16 from both sides

Next, we subtract 16 from both sides of the inequality \(-12 \leq 16 + 4x\). Doing so, we get \(-12 - 16 \leq 4x\), which simplifies to \(-28 \leq 4x\).

Step3: Divide by 4

Now, we divide both sides of the inequality \(-28 \leq 4x\) by 4. This results in \(-7 \leq x\), or equivalently \(x \geq -7\).

Now we check each option:

• For \(x = -10\): \(-10 \geq -7\) is false.
• For \(x = -9\): \(-9 \geq -7\) is false.
• For \(x = -8\): \(-8 \geq -7\) is false.
• For \(x = -7\): \(-7 \geq -7\) is true.

Answer:

D. \(-7\)