Solve for x: 10⋅x + 4 = 6⋅x -- 8. What is the value of x?

To solve the equation (10x + 4 = 6x - 8), we want to isolate the variable (x) by rearranging the equation.

First, subtract (6x) from both sides to get all terms involving (x) on one side:

[

10x - 6x + 4 = -8

]

This simplifies to:

[

4x + 4 = -8

]

Next, subtract (4) from both sides to move the constant term to the right side:

[

4x = -8 - 4

]

This simplifies to:

[

4x = -12

]

Now, divide both sides by (4) to solve for (x):

[

x = \frac{-12}{4} = -3

]

Thus, the value of (x) is (-3). This confirms that the correct option was selected. The process involves straightforward algebraic manipulation, which helps in systematically isolating the variable. Understanding how to balance equations and perform operations on both sides is crucial for solving similar problems in the future.