4x + 4 = 2x - 6

To solve 4x+4=2x-6.

This is a simple equation in one  unknown (or variable x). We have to find the value of  the unknown x.

We employ a technic of shifting all the unknowns, i.e. x's to the left and all the knowns or the numbers to the right, by simple operations like adding equals to both sides, or subtracting equals from both sides , or multiply by equals both sides , or dividing by equals both sides,(except dividing by zero) .

Subract 2x from both sides.

4x+4-2x= 2x-6-2x

Simplify by collecting the like terms, 4x and -2x on the left which gives 2x. On the right 2x and -2x  are the like terms and they get cancelled.

2x+4=-6

Subtrat 4 from both sides:

2x+4-4=-6-4.

Simplify both sides:

2x=-10.

Divide both sides by 2

2x/2=-10/2.

Simplify both sides.

x=-5.

Verification: Substititute the solution x=-5 in the given equation and see whether both sides become equal in value:

Left side : 4x+4= 4*(-5)+4=-20+4=-16

Right side:2x-6=2*(-5)-6 = -10-6=-16.