Question

Could someone help me learn how to do this?? I will give a medal and fan to whoever help me learn the best!
Solve the proportion 2x/5x + 6 = 2/x

Answer 1

x = -1 and x = 6

x = -1 and x = -6

x = 1 and x = -5

x = 1 and x = 5

Answer 2

@robz8

Answer 3

so you're looking for \[\frac{ 2x }{ 5x+6 } = \frac{ 2 }{ x }\]?

Answer 4

Okay, so it's

\[\frac{2x}{5x+6} = \frac{2}{x}\]

Answer 5

Okayy!

Answer 6

cross multiply and solve for x

Answer 7

Cross multiply?

Answer 8

it's a way to get rid of the denominators by multiplying both sides of the equation by both of the denominators

Answer 9

you end up with 2x^2 = 10x +12

Answer 10

then move everything to one side

2x^2 - 10x - 12

divide everything by 2

x^2 - 5x - 6

factor

(x-6)(x+1)

which means x = 6 and -1


a faster way to answer that would just be to plug in the x values in the answers and see which pair worked :P

Answer 11

Thank you as always!!