Question

What are the solutions for x in the proportion 5x-6/x=2x/x ?

x = −12 and x = −8

x = 12 and x = 8

x = −2 and x = −3

x = 2 and x = 3

Answer 1

How do you solve a proportion?

Answer 2

cross multipy. which would give me 5x-6(x)=2x(x)

Answer 3

Careful. (5x) (x) = (2x)(x) =

Answer 4

5x^2 & 2X^2?

Answer 5

Right. Now gather like terms and solve. If you are left with x^2 terms gather everything on one side and factor. What do YOU get?

Answer 6

This is always the part i don't understand. I didn't get it in the lesson. can you explain to me how to actually find the answers after all of that?

Answer 7

5x^2 -6x = 2x^2

Gather x^2 on same side.

3x^2 -6x = 0

Agree?

Answer 8

yes

Answer 9

Get a GCF for the two terms and factor it outside the parentheses. Whadda ya git?

Answer 10

45

Answer 11

GCF=3 but i don't see how i would factor that... 3[(x^2-2x)]

Answer 12

Now we can also factor out x. 3x ( x -2).

What x makes 3x=0? What x makes (x-2) = 0?

These are possible answers. You have to check to be sure they work.

What happened now?

Answer 13

subtract the 3 and add the 2?

Answer 14

2 is good, but 3 times what =0

Answer 15

0

Answer 16

So we have two possibilities 2 and 0. Do both work in the original proportion?

Answer 17

it doesn't look lik it to me. i might have done my work wrong. plus 0 isnt an answer.

Answer 18

0 would cause division by 0, so it is no good. 2 definitely works, but 3 will not work even though it is part of the same answer as 2. Peculiar???

Answer 19

Very

Answer 20

My fancy calculator confirms OUR answer.