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