Question

How do you solve `8x-1=63`?

Answer 1

`x=8`

Explanation:

`"isolate "8x" by adding 1 to both sides of the equation"`

`8x=63+1=64`

`"divide both sides by 8"`

`(cancel(8) x)/cancel(8)=64/8rArrx=8`

`color(blue)"As a check"`

`(8xx8)-1=64-1=63larr"correct"`

Answer 2

x = 8

Explanation:

`8x = 63 + 1`
`8x = 64`
`x = 64/8`
`x = 8`

Answer 3

Using Addition/Subtraction, 'move' all the constants to one side of the equation, and then divide through by `x`'s coefficient to find `x=8`

Explanation:

Our goal is to get `x` by itself. We will do this by applying factors to both sides of the equation.

The first step is to get all constants to the opposite side of the equation as `x`. For this scenario, that means eliminating the '-1' from the left hand side (LHS) and doing the same operation to the right hand side (RHS). How will we eliminate the '-1'? By adding 1 to both sides. This preserves equality for both sides.

`8x-1color(red)(+1)=63color(red)(+1)`

`8xcolor(red)(+0)=63color(red)(+1)`

`8x=64`

Next, we need to eliminate `x`'s coefficient. You would normally do this by multiplying or dividing both sides of the equation. For our purposes, the coefficient is 8, so we will divide both sides by 8 to determine what `x` is equal to:

`(8x)/color(red)(8)=64/color(red)(8)`

`8/color(red)(8)x=64/color(red)(8)`

`color(red)(1)x=64/color(red)(8)`

`color(green)(x=8)`