Solve the inequalities for real x : `3x - 7 > 5x - 1`

Explanation

To solve the inequality \(3x - 7 > 5x - 1\), we will follow these steps:

### Step 1: Rearrange the inequality
We start with the given inequality:
\[ 3x - 7 > 5x - 1 \]
To isolate the variable \(x\), we will move all terms involving \(x\) to one side and constant terms to the other side.

### Step 2: Subtract \(3x\) from both sides
Subtract \(3x\) from both sides:
\[ 3x - 7 - 3x > 5x - 1 - 3x \]
This simplifies to:
\[ -7 > 2x - 1 \]

### Step 3: Add 1 to both sides
Next, we add 1 to both sides to isolate the term with \(x\):
\[ -7 + 1 > 2x - 1 + 1 \]
This simplifies to:
\[ -6 > 2x \]

### Step 4: Divide by 2
Now, we divide both sides by 2 to solve for \(x\):
\[ \frac{-6}{2} > \frac{2x}{2} \]
This gives us:
\[ -3 > x \]
or equivalently:
\[ x < -3 \]

### Final Answer
The solution to the inequality is:
\[ x < -3 \]