Question

Determine o valor de X nas proporções a seguir

a) 2/15 = 3/2x

b) 9/4 = x+2/x+3

c)x+5/x = 10/8

d) 3x/21 = 5/7

e) 2x-1/x+2 = 3/5

f) x-5/3 = x-1/4

Answer 1

`a) x=(4)/(45)[\\\\b) x=-(19)/(5)\\\\c)x=20\\\\d)x=5\\\\e)x=(11)/(7)\\\\f) x=17`

Explanation:

a) Given the proportion:

`(2)/(15)=(3)/(2)x`

You must solve for "x":

`((2)/(3))((2)/(15))=x\\\\x=(4)/(45)`

b) Given:

`(9)/(4)=(x+2)/(x+3)`

Solve for "x":

`(x+3)((9)/(4))=x+2\\\\(9)/(4)x+(27)/(4)=x+2\\\\(9)/(4)x-x=2-(27)/(4)\\\\(5)/(4)x=-(19)/(4)\\\\x=(-(19)/(4))((4)/(5))\\\\x=-(19)/(5)`

c)
`(x+5)/(x)=(10)/(8)`

Solve for "x":

`x+5=(10)/(8)x\\\\5=(10)/(8)x-x\\\\5=(1)/(4)x\\\\(5)(4)=x\\\\x=20`

d)
`(3x)/(21)=(5)/(7)`

Solve for "x":

`3x=((5)/(7))(21)\\\\x=(15)/(3)\\\\x=5`

e)
`(2x-1)/(x+2)=(3)/(5)`

Solve for "x":

`(5)(2x-1)=(3)(x+2)\\\\10x-5=6x+6\\\\10x-3x=6+5\\\\7x=11\\\\x=(11)/(7)`

f)
`(x-5)/(3)=(x-1)/(4)`

Solve for "x":

`(4)(x-5)=(x-1)(3)\\\\4x-20=3x-3\\\\4x-3x=-3+20\\\\x=17`