Solve 2x – 4(x + 3) ≥ 4 + 3(4 – 3x).  

Let's solve the inequality \(2x - 4(x + 3) \geq 4 + 3(4 - 3x)\).

### Step 1: Expand both sides
Expand the expressions on both sides of the inequality.

- Left side:  
\[
2x - 4(x + 3) = 2x - 4x - 12 = -2x - 12
\]

- Right side:  
\[
4 + 3(4 - 3x) = 4 + 12 - 9x = 16 - 9x
\]

Thus, the inequality becomes:
\[
-2x - 12 \geq 16 - 9x
\]

### Step 2: Move the variables to one side
Add \(9x\) to both sides to collect the variable terms on one side.

\[
-2x + 9x - 12 \geq 16
\]
This simplifies to:
\[
7x - 12 \geq 16
\]

### Step 3: Isolate the variable
Add \(12\) to both sides to move the constants to the right side.

\[
7x \geq 28
\]

### Step 4: Solve for \(x\)
Divide both sides by 7.

\[
x \geq 4
\]

### Final Answer:
The solution to the inequality is:
\[
x \geq 4
\]

Do you want details or have any questions?

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Here are 5 related questions:
1. How do you solve an equation involving absolute values?
2. What is the process to solve compound inequalities?
3. How do you graph the solution of an inequality on a number line?
4. Can inequalities have multiple solutions? If yes, how?
5. How do you handle inequalities involving fractions?

**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 inequality 2x – 4(x + 3) ≥ 4 + 3(4 – 3x) step-by-step with detailed explanations and examples. This problem involves solving algebraic inequalities, suitable for advanced high school students (Grades 9-12).

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