https://file.aiquickdraw.com/mathbot/file/17254157514209toffnzv.jpg

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.

Solve the inequality -2 - (-4x - 6) ≤ -7x - 3

Understand how to solve the algebraic inequality -2 - (-4x - 6) ≤ -7x - 3 with a step-by-step guide. This lesson focuses on core algebraic concepts, including simplifying expressions and solving linear inequalities. Suitable for students in Grades 7-9.

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