Homework Help: Solve for x 5/3 = 1/2(x^-1)(y)

1. Jan 25, 2013

939

1. The problem statement, all variables and given/known data

Solve for x. I know how to do this when there is addition and subtraction but I'm confused what to do when there is multiplication. Sorry for the newb question...

2. Relevant equations

5/3 = 1/2(x^-1)(y)

3. The attempt at a solution

10/3 = (x^-1)(y)
(10/3)/(y) = (x^-1)

Last edited: Jan 25, 2013
2. Jan 25, 2013

Staff: Mentor

Is this 5/3 = 1/2 * x-1 * y?

If so, for starters, multiply both sides of the equation by x.

3. Jan 25, 2013

939

Yes, it is, sorry...

5/3(x) = (1/2)*(y)
then... divide both sides by 5/3?

x = 3/10(y)

Last edited: Jan 25, 2013
4. Jan 25, 2013

Staff: Mentor

Right, but this would be clearer as 3y/10.
If you write it as you did, some might (mistakenly) think you meant 3/[10y].

Also, dividing by 5/3 is the same as multiplying by 3/5, the reciprocal of 5/3.

5. Jan 25, 2013

939

Got it. Thanks yet again.

6. Jan 25, 2013

SpaceDreamer

You are trying to solve for x so my approach would be to solve to y in terms of x and then plug that into y so there is only x in the equation and then solve for x, so

5/3 = 1/2 * x^-1 * y
Multiply both sides by x as you did before
5/3x = 1/2 * y
Divide both sides by 1/2
10/3x = y

Now plug that into the original equation for y and then solve for x.

5/3 = 1/2 * x^-1 * (10/3x)

Solve for x. If my math is wrong please correct me, it's been some time since I done a problem like this.

7. Jan 25, 2013

tms

Do that and you'll find that 5/3 = 5/3.

8. Jan 26, 2013

Staff: Mentor

Since the instructions are to solve for x, it's a waste of time to solve for y first. All you need to do is get rid of the 5/3 coefficient of x, which you can do by multiplying both sides by 3/5. This leaves you with x = 3y/10, as before.