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?

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!