Question

Solve the inequality
1. 6w - 4 less than or equal to 2(3w + 6)

Answer 1

We start with the inequality:

\[
6w - 4 \leq 2(3w + 6)
\]

First, we distribute the 2 on the right side:

\[
6w - 4 \leq 6w + 12
\]

Next, we want to isolate the variable \(w\). We can start by subtracting \(6w\) from both sides:

\[
6w - 6w - 4 \leq 6w - 6w + 12
\]

This simplifies to:

\[
-4 \leq 12
\]

This statement is always true. Therefore, the inequality holds for all values of \(w\).

Thus, the solution to the inequality is:

\[
\text{All real numbers } w
\] or in interval notation, it can be expressed as:

\[
(-\infty, \infty)
\]