Question

How do you solve for x in `8ax-7a^2=19a^2-5ax`?

Answer 1

`x = 2a`

Explanation:

`8ax - 7a^2 = 19a^2 - 5ax`

Collecting like terms;

Note: When crossing over a Negative value or unknown in a algebraic expression, the sign changes the the Positive value, also when crossing over a Positive value or uknown the sign changes to a Negative value, (Vice-Versa)

`8ax + 5ax = 19a^2 + 7a^2`

Simplifying;

`13ax = 26a^2`

Dividing both sides by the coefficient of `x`;

`(13ax)/(13a) = (26a^2)/(13a)`

`(cancel(13a)x)/cancel(13a) = (26a^2)/(13a)`

`x = (26a^2)/(13a)`

`x = (2a xx 13a)/(13a)`

`x = (2a xx cancel(13a))/cancel(13a)`

`x = (2a)/1`

`x = 2a`

Answer 2

`x=2a`

Explanation:

`"collect terms in x together on the left side and other"`
`"terms on the right side"`

`"add "5ax" to both sides"`

`8ax+5ax-7a^2=19a^2cancel(-5x)cancel(+5x)`

`13ax-7a^2=19a^2`

`"add "7a^2" to both sides"`

`13ax=19a^2+7a^2`

`13ax=26a^2`

`"divide both sides by "13a`

`(cancel(13a) x)/cancel(13a)=(26a^2)/(13a)rArrx=2a`