MATH HELP Me?

Question

Solve the proportion.Check for extraneous solutions.

x+6/3=x-5/2 and this one d/d+4=d-2/d

This isn't my hw so no stupid comments! and please explain how you did it and if you don't know how to do it then don't even answer

Answer 1

I think you mean (x + 6)/3 = (x - 5)/2, because otherwise that first one wouldn't be possible no matter WHAT x was.

OK, simple. All you have to do is multiply through by 3, then multiply through by 2. This gets rid of the denominators. It's also called cross-multiplying, but it makes more sense if you do it all out the first time.
So, multiply both sides of the equation by 3. On the left side, the 3 cancels with the 3 in the denominator, so you have just x + 6. On the right side, though, the 3 gets multiplied by the numerator so you have 3(x - 5)/2. So now you have

x + 6 = 3(x - 5)/2
OK, now what? Well, you want to get rid of that pesky denominator on the right side. Then it's easy - you can just expand and solve. So multiply through by 2:

2(x + 6) = 3(x - 5)
OK, NOW expand and solve.
2x + 12 = 3x - 15
Subtract 2x from both sides....
12 = x - 15
And add 15 to both sides.
27 = x
That's your answer!

As for the second one... again i'm going to assume it's actually d/(d + 4) = (d - 2)/d because it's much simpler that way. OK, do the same thing!

First, multiply through by (d + 4), because it's on the bottom on the left side... It cancels on the left side, so you're left with d, and on the right side you have (d + 4)(d - 2)/d. If this confuses you, just compare it with the last example. It's exactly the same, except instead of numbers I'm using things like d + 4 and d - 2.

So now you have
d = (d + 4)(d - 2)/d
OK, now you want to get rid of the denominator on the RIGHT side. So multiply by d on both sides of the equation:
d^2 = (d + 4)(d - 2)
OK, expanding this is a little harder. Remember how to foil?
d^2 = d^2 - 2d + 4d - 8
Subtract d^2 from both sides, and combine like terms
0 = 2d - 8
Add 8 to both sides
2d = 8
Divide both sides by 2
d = 4

There's your answer.
Doesn't look like there are any mess-ups when you sub these values back into the equations, so I think we're good.

P.S. The guy before me is right - you left out the parentheses in your expressions, so they don't make sense. In my solutions, I assumed the parentheses were there even though they weren't, and went from there. You should be careful - d + 5/d means something different from (d + 5)/d.

Answer 2

It may not be your homework, but I dont see any proportions, either. With the x equation, it is not consistent. The second one is 5=d-2/d,
Then 5d= d^2-2 and d^2-5d-2= 0 . You can solve this with the quadratic equation (5+/- sqrt(33))/2.

If you examine the original equation, you will see that d is somewhere between 5 and 6. So the -sqrt root IS extraneous, since you introduced it in by the multiplication to get the quadratic.

Answer 3

(x + 6)/3 = x - 5/2 multiply both sides by 3

x+6 = 3x -15/2 multiply both sides by 2

2x + 12 = 6x -15

-4x = -27

x = 6.75

substitute back into equation

(6.75 + 6) /3 = 6.75 - 2.50

4.25 = 4.25

Answer 4

cross multiply

2x+12 = 3x -15

x = 27

d^2 = d^2+2d-8

d = 4

Answer 5

STUPID COMMENTS ha look who needs help in math