Question

How do you solve `4( x - 2) = 10x - 40`?

Answer 1

`color(green)(x=5 1/3)`

Explanation:

Applying the distributive property
`4(x-2)` = 4x+4xx(-2) = 4x-8#

So `4(x-2)=10x-40`
is equivalent to
`color(white)("XXX")4x-8=10x-40`

subtracting `4x` from both sides gives
`color(white)("XXX")-8=6x-40`

then adding `40` to both sides:
`color(white)("XXX")32=6x`

finally, dividing both sides by `6`
`color(white)("XXX")5 1/3 =x" or " x= 5 1/3`

Answer 2

`x=16/3`

Explanation:

To solve collect terms in x to one side of the equation and numeric values to the other side.

distribute the bracket to begin with.

`rArr4x-8=10x-40`

subtract 4x from both sides.

`cancel(4x)cancel(-4x)-8=10x-4x-40`

`rArr-8=6x-40`

add 40 to both sides.

`-8+40=6xcancel(-40)cancel(+40)`

`rArr6x=32`

To solve for x, divide both sides by 6

`(cancel(6) x)/cancel(6)=32/6`

`rArrx=16/3" is the solution"`