algebra help!!!

[ElizK]

It's been WAY too many years since I've done this kind of math. If there were an example in DD14's book I could figure it out, but no example. Could someone show me step by step how to cross multiply this to solve for x??? I would be eternally greatful!


2/x-3 = 5/x+1

 

[damo]

Is just the x under the 2 and 5 or are x-3 and x+1 the denominators?

 

[ElizK]

Is just the x under the 2 and 5 or are x-3 and x+1 the denominators?

sorry, that was unclear. x-3 and x+1 are the denominators

 

[TheDisneyTraveler06]

Try math.com to see if that can help you.

 

[Madaboutthemouse]

_2 _ = _5_
x-3 x+1

Okay, well, I can't quite get the problem formatted correctly, but oh well.
Anyways, when I teach this concept, I have my kids draw a big X on the equal sign in the problem...it connects the left numerator with the right denominator and the right numerator with the left denominator. This shows which terms are going to be "cross multiplied". The 2 and the (x+1) will be multiplied together and the 5 and the (x-3).

2(x + 1) = 2x + 2 (using the distributive property - you have to multiply the 2 by everything inside the parentheses)
5(x - 3) = 5x - 15 (again using the dist. prop.)

So...
2x + 2 = 5x - 15
2 = 3x - 15 (subtract 2x from both sides to get the x terms together)
17 = 3x (add 15 to both sides to get the numerical terms together)
x = 17/3 or 5 and 2/3 (divide both sides by 3 to simplify)

 

[Fannie_Marie]

well, I guess I did the problem wrong! : As always, once it's worked out it seems so simple!

 

[HappyDznyCamper]

5(x-3)=2(x+1)
5x-15=2x+2
3x-15=2
3x/3=17/3
x=5 2/3

 

[ElizK]

_2 _ = _5_
x-3 x+1

Okay, well, I can't quite get the problem formatted correctly, but oh well.
Anyways, when I teach this concept, I have my kids draw a big X on the equal sign in the problem...it connects the left numerator with the right denominator and the right numerator with the left denominator. This shows which terms are going to be "cross multiplied". The 2 and the (x+1) will be multiplied together and the 5 and the (x-3).

2(x + 1) = 2x + 2 (using the distributive property - you have to multiply the 2 by everything inside the parentheses)
5(x - 3) = 5x - 15 (again using the dist. prop.)

So...
2x + 2 = 5x - 15
2 = 3x - 15 (subtract 2x from both sides to get the x terms together)
17 = 3x (add 15 to both sides to get the numerical terms together)
x = 17/3 or 5 and 2/3 (divide both sides by 3 to simplify)

You are awesome!! Thank you so much. I worked through it as you showed and figured it out. Can't thank you enough!

 

[jcsbama]

Oops, wait, I realized I forgot a multiplication. Now I correct it.

I come up with 5 2/3 as the answer. If you cross multiply, you get
2x+2 = 5x-15
Whatever you do on one side of the equation, you have to do on the other side. You want to isolate the x on one side. If I subtract 2x from the first side, I have to do the same on the other side. The equation then looks like this:
2 = 3x-15
Do the same thing again except add 15 to both sides to get:
17 = 3x
Divide by 3 and you have the answer for x.

I think this is right. If not, I'm sure someone will correct me.

 

[Madaboutthemouse]

You are awesome!! Thank you so much. I worked through it as you showed and figured it out. Can't thank you enough!

No problem! I teach 7th and 8th grade Math and my own students struggle with this too! Glad I could help!