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

## Homework Statement

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...

## Homework Equations

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

## The Attempt at a Solution

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

Last edited:

Mark44
Mentor

## Homework Statement

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...

## Homework Equations

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

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

## The Attempt at a Solution

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

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

If so, for starters, multiply both sides of the equation by x.
Yes, it is, sorry...

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

x = 3/10(y)

Last edited:
Mark44
Mentor
Yes, it is, sorry...

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

x = 3/10(y)
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.

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.

Got it. Thanks yet again.

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.

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

Mark44
Mentor
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
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.
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.