Question

How do you solve `1 /( 4 x + 2) = 5` and find any extraneous solutions?

Answer 1

`x=-9/20`

Explanation:

Eliminate the fraction on the left side of the equation by multiplying both sides by (4x +2) the denominator of the fraction.

`rArrcancel((4x+2))xx1/cancel((4x+2))=5(4x+2)`

`rArr1=20x+10`

subtract 10 from both sides.

`1-10=20xcancel(+10)cancel(-10)`

`rArr20x=-9`

To solve for x, divide both sides by 20

`(cancel(20) x)/cancel(20)=(-9)/20`

`rArrx=-9/20" is the only solution"`