Example

`4(2x−6)+9=3(x−7)+8x`	Distribute `4` and `3` through parenthesis
`8x−24+9=3x−21+8x`	Combine like terms`−24+9` and `3x+8x`
`8x− 15 = 11x − 21 `	Notice the variable is on both sides
`8xcolor(red)(-8x)− 15 = 11xcolor(red)(-8x) − 21`	Subtract `8x` from both sides
`− 15 = 3x − 21`	Focus on subtraction of `21`
`− 15color(red)(+21) = 3x − 21color(red)(+21)`	Add `21` to both sides
`6=3x`	Focus on multiplication by `3`
`6/color(red)(3)=(3x)/color(red)(3)`	Divide both sides by `3`
`2=x `	Solution

There are two special cases that can come up as we are solving these linear equations. The first is illustrated in the next two examples. Notice we start by distributing and moving the variables all to the same side. Example

`3(2x − 5) = 6x − 15`	Distribute `3` through parenthesis
`6x − 15 = 6x − 15`	Notice the variable on both sides
`6x − 15 = 6x − 15`	Subtract `6x` from both sides
`-15=-15 `	Variable is gone! True!

Here the variable subtracted out completely! We are left with a true statement, `− 15 = − 15`. If the variables subtract out completely and we are left with a true statement, this indicates that the equation is always true, no matter what x is. Thus, for our solution we say all real numbers or `R`. Example

`2(3x−5)−4x=2x+7`	Distribute `2` through parenthesis
`6x−10−4x=2x+7`	Combine like terms `6x−4x`
`2x-10=2x+7`	Notice the variable is on both sides
`2x-10=2x+7`	Subtract `2x` from both sides
`-10≠7`	Variable is gone! False!

Again, the variable subtracted out completely! However, this time we are left with a false statement, this indicates that the equation is never true, no matter what x is. Thus, for our solution we say no solutionor `∅`.