Question

Which inequality represents the solution to 1/4 (8x-12)<6+x


?
x<6
x<9
x>6
x>9

Answer 1

To solve the inequality \(\frac{1}{4}(8x - 12) < 6 + x\), we can start by distributing \(\frac{1}{4}\) on the left side:

\[
\frac{1}{4} \cdot 8x - \frac{1}{4} \cdot 12 < 6 + x
\]

This simplifies to:

\[
2x - 3 < 6 + x
\]

Next, we can isolate \(x\) by subtracting \(x\) from both sides:

\[
2x - x - 3 < 6
\]

This simplifies to:

\[
x - 3 < 6
\]

Now, add 3 to both sides to solve for \(x\):

\[
x < 6 + 3
\]

This simplifies to:

\[
x < 9
\]

So the correct inequality that represents the solution is:

\[
x < 9
\]

The answer is \(x < 9\).