https://file.aiquickdraw.com/mathbot/file/1726895537520kqs4v2rj.jpg

The inequality to solve is:

\[
-4(x - 3) - 4x < -(2x + 15) + 3x
\]

Let's break it down step by step.

### Step 1: Expand both sides
Expand the expressions on both sides:

\[
-4(x - 3) = -4x + 12
\]
Thus, the inequality becomes:

\[
(-4x + 12) - 4x < -(2x + 15) + 3x
\]

### Step 2: Simplify both sides
Simplify the left side:

\[
-4x + 12 - 4x = -8x + 12
\]

Now simplify the right side:

\[
-(2x + 15) + 3x = -2x - 15 + 3x = x - 15
\]

So, the inequality is now:

\[
-8x + 12 < x - 15
\]

### Step 3: Isolate the variable
Move all terms involving \( x \) to one side:

\[
-8x - x < -15 - 12
\]
\[
-9x < -27
\]

### Step 4: Solve for \( x \)
To solve for \( x \), divide both sides by \( -9 \), remembering to reverse the inequality sign when dividing by a negative number:

\[
x > 3
\]

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

\[
x > 3
\]

Would you like any further details on this? Here are some related questions:

1. How do you solve inequalities with fractions?
2. What are the key differences between solving equations and inequalities?
3. How do you handle absolute value inequalities?
4. Can inequalities have more than one solution set?
5. How do you graph solutions to inequalities on a number line?

**Tip:** When dividing or multiplying both sides of an inequality by a negative number, always reverse the inequality sign.

Solve the inequality -4(x - 3) - 4x < -(2x + 15) + 3x.

Learn how to solve the linear inequality -4(x - 3) - 4x < -(2x + 15) + 3x with a step-by-step explanation. This covers key algebraic concepts such as expanding expressions, combining like terms, and applying the sign reversal rule when dividing by negative numbers. Suitable for students in Grades 8-10.

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