Question

What value of x is in the solution set of the inequality 4x – 12 ≤ 16 + 8x?

–10
–9
–8
–7

Answer 1

To solve the inequality \( 4x - 12 \leq 16 + 8x \), we will first isolate \( x \).

1. Start by moving all terms involving \( x \) to one side and constant terms to the other side:
\[
4x - 8x \leq 16 + 12
\]

2. This simplifies to:
\[
-4x \leq 28
\]

3. Now, divide both sides by -4. Remember that when dividing by a negative number, we need to flip the inequality sign:
\[
x \geq -7
\]

The solution set indicates that \( x \) can be any value greater than or equal to -7.

Now we can check which values from the provided options satisfy the inequality:
- **–10**: Not included (since –10 < -7)
- **–9**: Not included (since –9 < -7)
- **–8**: Not included (since –8 < -7)
- **–7**: Included (since –7 = -7)

Thus, the value of \( x \) in the solution set of the inequality is:
\[
\boxed{-7}
\]