Question

Help. 20 points. this is a proportion question.
what does x = ?

Answer 1

x = 7

Explanation:

`(3)/(x)=(x-4)/(7)`

==> cross multiply

`3*7=x*(x-4)`

==> simplify

21 = x² - 4x

==> subtract 21 from both sides

0 = x² - 4x - 21

==> factorize by finding two numbers that multiply to -21 and add up to equal -4

0 = (x - 7)(x + 4)

==> set each factor to 0 and solve for x

0 = (x - 7) 0 = (x + 4)

7 = x -4 = x

We can now plug in the values of x into the proportion to see which are true.

`(3)/(x)=(x-4)/(7)`
`(3)/(x)=(x-4)/(7)`

x = 7 x = - 4

`(3)/(7)=(7-4)/(7)`
`(3)/(-4)=(-4-4)/(7)`

==> subtract 4 from 7 ==> subtract -4 from -4

`(3)/(7)=(3)/(7)`
`-(3)/(4)=-(8)/(7)`

The only true answer is x = 7