Question

How do you solve `7+8x=63`?

Answer 1

`x=7`

Explanation:

`7+8x=63`

`8x=63 -7`

`8x=56`

`x=56/8`

`x=7`

Answer 2

The others have shown you the shortcut method. This is the same thing but from first principles.

`x=7`

Explanation:

Given:`" "color(brown)(7+8x=63)`

The objective is to have just one `x` and for that to be on one side of the equals sign and everything else on the other side. In doing this you are saying: This is what one `x` is 'worth' (its value).

`color(blue)("Step 1")`
`color(brown)("Have all the terms with x in them on one side and everything else on the other")`

So we need to 'get rid of the 7 on the left side
We do this by turning it into zero. The thing is; what you do to one side you do to the other to keep numeric balance.

Subtract `color(blue)( 7)` from both sides

`color(brown)(7color(blue)(-7) +8x=63color(blue)(-7))`

`0+8x=56`

`8x=56`

`color(blue)("Step 2")`

Divide both sides by 8. This is the same as `color(blue)(xx1/8)`

`color(brown)(8xcolor(blue)(xx1/8)= 56color(blue)(xx1/8))`

`8/8 x=56/8`

But `8/8 =1` giving

`color(magenta)(x=56/8=7)`