Question

How do you solve `\frac { x + 4} { x - 2} = \frac { 1} { 4}`?

Answer 1

`x=-6`

Explanation:

When we have a fraction equal to another fraction, we can solve using the method of `color(blue)"cross-multiplication"`

That is `color(red)(x+4)/color(blue)(x-2)=color(blue)(1)/color(red)(4)`

Now multiply the terms on either end of an 'imaginary' cross (X) placed on top of the = sign and equate them.

That is, multiply the terms in `color(red)"red"` together, the terms in `color(blue)"blue"` together and equate them.

`color(red)(4(x+4))=color(blue)(1(x-2)`

distribute the brackets.

`rArr4x+16=x-2`

subtract x from both sides.

`4x-x+16=cancel(x)cancel(-x)-2`

`rArr3x+16=-2`

subtract 16 from both sides.

`3xcancel(+16)cancel(-16)=-2-16`

`rArr3x=-18`

To solve for x, divide both sides by 3.

`(cancel(3) x)/cancel(3)=(-18)/3`

`rArrx=-6" is the solution"`