https://file.aiquickdraw.com/mathbot/file/1727187111963zxj506x6.jpg

The inequality shown in the image is:

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

Let's solve this step by step.

### Step 1: Subtract \(2x\) from both sides
\[
4x - 2x + 2 \leq -2
\]
\[
2x + 2 \leq -2
\]

### Step 2: Subtract 2 from both sides
\[
2x \leq -2 - 2
\]
\[
2x \leq -4
\]

### Step 3: Divide both sides by 2
\[
x \leq \frac{-4}{2}
\]
\[
x \leq -2
\]

### Final Answer:
\[
x \leq -2
\]

The solution to the inequality is \(x \leq -2\). 

Do you have any questions or need further details? 

Here are some related questions you might find helpful:
1. How do you graph the solution \(x \leq -2\) on a number line?
2. Can you provide examples of inequalities that involve absolute values?
3. What changes when dividing or multiplying inequalities by negative numbers?
4. How do inequalities differ from equations in terms of solutions?
5. How would you solve a compound inequality involving both \(x \geq a\) and \(x \leq b\)?

**Tip:** When solving inequalities, remember to reverse the inequality sign if you multiply or divide both sides by a negative number.

Learn how to solve the linear inequality 4x + 2 ≤ 2x - 2 with a detailed step-by-step solution. This problem involves simplifying both sides of the inequality, performing algebraic operations, and understanding the properties of inequalities. Suitable for students in Grades 7-9.

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