`3(1 - x ) lt 2 (x + 4)`

Explanation

To solve the inequality \(3(1 - x) < 2(x + 4)\), we will follow these steps:

### Step 1: Distribute the terms in the inequality
We start by distributing the constants on both sides of the inequality.

\[ 3(1 - x) < 2(x + 4) \]

This expands to:

\[ 3 - 3x < 2x + 8 \]

### Step 2: Rearrange the inequality
Next, we will move all terms involving \(x\) to one side and constant terms to the other side.

Add \(3x\) to both sides:

\[ 3 < 2x + 3x + 8 \]

This simplifies to:

\[ 3 < 5x + 8 \]

Now, subtract \(8\) from both sides:

\[ 3 - 8 < 5x \]

This simplifies to:

\[ -5 < 5x \]

### Step 3: Divide by 5
Now, we will divide both sides by \(5\) to isolate \(x\):

\[ \frac{-5}{5} < x \]

This simplifies to:

\[ -1 < x \]

### Step 4: Write the final solution
We can rewrite the inequality as:

\[ x > -1 \]

In interval notation, this means:

\[ x \in (-1, \infty) \]

### Final Answer:
The solution to the inequality \(3(1 - x) < 2(x + 4)\) is \(x > -1\) or in interval notation, \(x \in (-1, \infty)\).

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