What is the value of x in the equation 5x - 2 = 3x + 10?

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

1. Begin by moving the terms involving ( x ) to one side. Subtract ( 3x ) from both sides:

[

5x - 3x - 2 = 10

]

This simplifies to:

[

2x - 2 = 10

]

2. Next, add 2 to both sides to eliminate the constant on the left side:

[

2x - 2 + 2 = 10 + 2

]

This results in:

[

2x = 12

]

3. Finally, divide each side by 2 to solve for ( x ):

[

x = \frac{12}{2}

]

Which simplifies to:

[

x = 6

]

The solution ( x = 6 ) is therefore the correct answer. This value satisfies the original