Which of the following option is satisfied for the value of `2x-3 gt 7-x`?

Options

A. `x= (10)/(3)`
B. `x lt (10)/(3)`
C. `x gt 4`
D. `x gt (10)/(3)`

Answer

To solve the inequality \(2x - 3 > 7 - x\), 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.

\[ 2x - 3 > 7 - x \]

Add \(x\) to both sides:

\[ 2x + x - 3 > 7 \]

This simplifies to:

\[ 3x - 3 > 7 \]

### Step 2: Isolate the \(x\) term
Next, add 3 to both sides to isolate the term with \(x\):

\[ 3x - 3 + 3 > 7 + 3 \]

This simplifies to:

\[ 3x > 10 \]

### Step 3: Solve for \(x\)
Now, divide both sides by 3 to solve for \(x\):

\[ x > \frac{10}{3} \]

### Conclusion
The solution to the inequality \(2x - 3 > 7 - x\) is:

\[ x > \frac{10}{3} \]