Which of the following is a solution of `2x -5 gt 4x -3`?

Options

A. 0
B. 1
C. `-1`
D. `-2`

Answer

To solve the inequality \(2x - 5 > 4x - 3\), we will follow these steps:

### Step 1: Rearrange the inequality
Start by moving all terms involving \(x\) to one side and constant terms to the other side.

\[ 2x - 5 > 4x - 3 \]

Subtract \(4x\) from both sides:

\[ 2x - 4x - 5 > -3 \]

This simplifies to:

\[ -2x - 5 > -3 \]

### Step 2: Isolate the term with \(x\)
Next, we will isolate the term with \(x\) by adding \(5\) to both sides:

\[ -2x > -3 + 5 \]

This simplifies to:

\[ -2x > 2 \]

### Step 3: Solve for \(x\)
Now, we need to solve for \(x\). To do this, divide both sides by \(-2\). Remember that when you divide by a negative number, the inequality sign reverses:

\[ x < \frac{2}{-2} \]

This simplifies to:

\[ x < -1 \]

### Conclusion
The solution to the inequality \(2x - 5 > 4x - 3\) is:

\[ x < -1 \]