Solve `2(x-3) + 4 ge 4 - x`

Answer

To solve the inequality \( 2(x - 3) + 4 \geq 4 - x \), we will follow these steps:

### Step 1: Expand the left side
Start by distributing the \( 2 \) in the expression \( 2(x - 3) \).

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

### Step 2: Simplify the left side
Combine like terms on the left side.

\[ 2x - 6 + 4 = 2x - 2 \]

Now, the inequality becomes:

\[ 2x - 2 \geq 4 - x \]

### Step 3: Move all terms involving \( x \) to one side
Add \( x \) to both sides of the inequality to get all \( x \) terms on the left side.

\[ 2x + x - 2 \geq 4 \]

This simplifies to:

\[ 3x - 2 \geq 4 \]

### Step 4: Isolate the \( x \) term
Add \( 2 \) to both sides to isolate the term with \( x \).

\[ 3x \geq 4 + 2 \]

This simplifies to:

\[ 3x \geq 6 \]

### Step 5: Solve for \( x \)
Divide both sides by \( 3 \) to solve for \( x \).

\[ x \geq \frac{6}{3} \]

This simplifies to:

\[ x \geq 2 \]

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

\[ x \geq 2 \]

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