How do you solve the inequality 3x + 2 ≤ 1?

To solve the inequality \(3x + 2 \leq 1\), follow these steps:

Step 1: Isolate the Variable

Begin by getting the term with \(x\) by itself. Subtract 2 from both sides:

\(3x + 2 - 2 \leq 1 - 2\)

Which simplifies to:

\(3x \leq -1\)

Step 2: Solve for \(x\)

Next, divide both sides by 3 to find \(x\):

\(x \leq -\frac{1}{3}\)

Step 3: Write the Solution

The solution to the inequality is:

\(x \leq -\frac{1}{3}\)

Graphical Representation

On a number line, this means you would shade all numbers to the left of \(-\frac{1}{3}\), including \(-\frac{1}{3}\) itself, which is represented with a closed dot.

Summary

• Subtract 2 from both sides.
• Divide by 3.
• Write the final answer as \(x \leq -\frac{1}{3}\).