https://file.aiquickdraw.com/mathbot/file/1726204377109yub6g32a.jpg

Let's solve the inequality from the image:

\[
4[5x - (3x - 6)] < 3(4x - 6)
\]

### Step 1: Simplify the expressions inside the brackets and parentheses

Start by simplifying the term inside the first bracket:

\[
5x - (3x - 6) = 5x - 3x + 6 = 2x + 6
\]

Now, substitute this back into the inequality:

\[
4(2x + 6) < 3(4x - 6)
\]

### Step 2: Distribute the constants

Distribute the 4 and the 3:

\[
4(2x) + 4(6) < 3(4x) - 3(6)
\]

This simplifies to:

\[
8x + 24 < 12x - 18
\]

### Step 3: Move terms involving \(x\) to one side and constants to the other side

Subtract \(8x\) from both sides:

\[
24 < 4x - 18
\]

Add 18 to both sides:

\[
42 < 4x
\]

### Step 4: Solve for \(x\)

Divide both sides by 4:

\[
x > \frac{42}{4} = 10.5
\]

### Final solution:

\[
x > 10.5
\]

Do you want further details or have any questions? 

Here are some related questions you could explore:
1. How do you check if the solution to the inequality is correct?
2. How do you solve inequalities with absolute values?
3. What happens if you multiply or divide both sides of an inequality by a negative number?
4. How would the solution change if it were a "greater than or equal to" inequality?
5. How can you graph the solution of this inequality on a number line?

**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 algebraic inequality 4[5x - (3x - 6)] < 3(4x - 6). This solution uses key algebraic techniques such as simplification and applying the distributive property, suitable for students in Grades 9-11.

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