Question

Solve the following inequalities for the variable,
x
x.
4
x
−
4
≤
2
x
+
6
4x−4≤2x+6

Answer 1

To solve the inequality \( 4x - 4 \leq 2x + 6 \), we will follow these steps:

1. **Move all terms involving \( x \) to one side** and constant terms to the other side. We can do this by subtracting \( 2x \) from both sides:

\[
4x - 2x - 4 \leq 6
\]

This simplifies to:

\[
2x - 4 \leq 6
\]

2. **Add 4 to both sides** to isolate the terms involving \( x \):

\[
2x - 4 + 4 \leq 6 + 4
\]

Simplifying gives us:

\[
2x \leq 10
\]

3. **Divide both sides by 2** to solve for \( x \):

\[
x \leq 5
\]

The solution to the inequality \( 4x - 4 \leq 2x + 6 \) is

\[
\boxed{x \leq 5}
\]