Solve for \(x\): \(5x - 3 = 2x + 10\).

To solve the equation (5x - 3 = 2x + 10), we want to isolate the variable (x) on one side.

First, we can start by moving all terms involving (x) to one side. This can be done by subtracting (2x) from both sides of the equation:

[

5x - 2x - 3 = 10

]

This simplifies to:

[

3x - 3 = 10

]

Next, to eliminate the constant on the left side, we add (3) to both sides:

[

3x - 3 + 3 = 10 + 3

]

This results in:

[

3x = 13

]

Now, to solve for (x), we divide both sides by (3):

[

x = \frac{13}{3}

]

When calculated, this is approximately (4.33). This corresponds to the option that provides the value (x = 4.33).

It's important to emphasize that accurately carrying out each algebraic operation step-by-step leads to the correct solution, and checking one's work at the end can further