The image provided shows a mathematical inequality that needs to be solved. The inequality is:

$-2 - (-4x - 6) \leq -7x - 3$

Let's solve the inequality step by step.

Step 1: Simplify the expression on the left side

First, distribute the negative sign inside the parentheses:

$-2 + 4x + 6 \leq -7x - 3$

Combine like terms on the left side:

$4x + 4 \leq -7x - 3$

Step 2: Isolate the variable

Next, let's add $7x$ to both sides to bring all the $x$ terms to the left:

$4x + 7x + 4 \leq -3$

This simplifies to:

$11x + 4 \leq -3$

Now, subtract 4 from both sides:

$11x \leq -7$

Step 3: Solve for $x$

Finally, divide both sides by 11:

$x \leq -\frac{7}{11}$

Solution

The solution to the inequality is:

$x \leq -\frac{7}{11}$

Would you like further details or have any questions?

Here are some related questions:

1. How do you solve an inequality involving fractions?
2. What happens to an inequality when you multiply or divide both sides by a negative number?
3. How can you graph the solution $x \leq -\frac{7}{11}$ on a number line?
4. What is the difference between solving equations and inequalities?
5. How do you check if your solution to an inequality is correct?

Tip: Always remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.