Which of the following is the solution set of `3x-7gt5x-1AAx in` R ?

Options

A. `(-oo,-3)`
B. `(-oo,-3]`
C. `(-3,oo)`
D. `(-3,3)`

Answer

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

### Step 1: Rewrite the inequality
We start with the given inequality:
\[ 3x - 7 > 5x - 1 \]

### Step 2: Move all terms involving \(x\) to one side
To isolate \(x\), we can subtract \(3x\) from both sides:
\[ -7 > 5x - 3x - 1 \]
This simplifies to:
\[ -7 > 2x - 1 \]

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

### Step 4: Divide by the coefficient of \(x\)
Now, we divide both sides by \(2\). Remember that since we are dividing by a positive number, the direction of the inequality remains the same:
\[ \frac{-6}{2} > x \]
This simplifies to:
\[ -3 > x \]
or equivalently,
\[ x < -3 \]

### Step 5: Write the solution set
The solution set in interval notation is:
\[ (-\infty, -3) \]

### Conclusion
Thus, the solution set of the inequality \(3x - 7 > 5x - 1\) is \((- \infty, -3)\).