Question

How do you solve `4x - 2 = 2x + 8`?

Answer 1

`x=5`

Explanation:

`color(blue)(4x)color(red)(-2)=color(blue)(2x)+color(red)8`

Bring like terms to one side:

`4x-2x=8+2`

`2x=10`

Divide both sides by `2`:

`x=5`

Answer 2

`x = 5`

Explanation:

`4x - 2 = 2x + 8`

We eleminate 2x on the right by substracting 2x from each side.
Equivalently, we can add -2x to both sides.
`4x - 2 color(red)( -2x) = 2x color(red)(-2x) +8`

Simplify
`2x -2 = 8`

Add 2 to each side.
`2x-2 color(red)(+2 )= 8 color(red)(+2)`

`2x = 10`

Multiply each side by 1/2
`2x color(red)(xx(1/2)) = 10 color(red)(xx 1/2`

`x =5`

Check !

`4x - 2 = 2x + 8` substitute x=5 into equation

`4(5) - 2 = 2(5) +8`
`20 - 2= 10 +8`
`18 = 18`