Find the solution set of `3x-10gt5x+1`.

Answer

To solve the inequality \(3x - 10 > 5x + 1\), we will follow these steps:

### Step 1: Rearrange the inequality
We start with the original inequality:
\[ 3x - 10 > 5x + 1 \]
To isolate \(x\), we will move all terms involving \(x\) to one side and constant terms to the other side. We can do this by subtracting \(5x\) from both sides:
\[ 3x - 5x - 10 > 1 \]
This simplifies to:
\[ -2x - 10 > 1 \]

### Step 2: Move the constant term
Next, we will add \(10\) to both sides to isolate the term with \(x\):
\[ -2x > 1 + 10 \]
This simplifies to:
\[ -2x > 11 \]

### Step 3: Divide by the coefficient of \(x\)
Now, we will divide both sides by \(-2\). Remember that when we divide or multiply by a negative number, we must reverse the inequality sign:
\[ x < \frac{11}{-2} \]
This simplifies to:
\[ x < -\frac{11}{2} \]

### Step 4: Write the solution set
The solution set can be expressed in interval notation. Since \(x\) can take any value less than \(-\frac{11}{2}\), we write:
\[ x \in (-\infty, -\frac{11}{2}) \]

### Final Answer
Thus, the solution set of the inequality \(3x - 10 > 5x + 1\) is:
\[ \boxed{(-\infty, -\frac{11}{2})} \]