https://file.aiquickdraw.com/mathbot/file/1727633970929rbh4s08w.jpg

The inequality shown in the image is:

\[
6x - 7 \leq 2x + 1
\]

Let's solve this step-by-step.

### Step 1: Move all terms involving \( x \) to one side of the inequality
We subtract \( 2x \) from both sides:

\[
6x - 7 - 2x \leq 2x + 1 - 2x
\]

This simplifies to:

\[
4x - 7 \leq 1
\]

### Step 2: Move the constant terms to the other side
We add 7 to both sides to eliminate the \(-7\):

\[
4x - 7 + 7 \leq 1 + 7
\]

This simplifies to:

\[
4x \leq 8
\]

### Step 3: Solve for \( x \)
Now, divide both sides by 4:

\[
x \leq \frac{8}{4}
\]

Simplifying:

\[
x \leq 2
\]

### Final Answer:
The solution to the inequality is:

\[
x \leq 2
\]

Would you like more details on this, or have any questions?

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Here are 5 related questions to deepen your understanding:

1. How do inequalities change when dividing by negative numbers?
2. Can you solve another inequality: \(3x + 5 > 2x - 4\)?
3. How would you represent the solution \(x \leq 2\) on a number line?
4. What happens to the inequality symbol if both sides are multiplied by \(-1\)?
5. Can inequalities have infinite solutions?

**Tip**: Always flip the inequality symbol when multiplying or dividing both sides by a negative number!

Learn how to solve the linear inequality 6x - 7 ≤ 2x + 1 with a detailed step-by-step explanation. This algebraic problem focuses on inequalities, simplifying terms, and solving for x. Suitable for students in Grades 8-10.

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