Question

I dont get this Rewrite the equation below so that it does not have fractions. 2-(3)/(4)x=(9)/(10) Do not use decimals in your answer.

Answer 1

Suppose we have an equation like:

`(A)/(C) = (B)/(D)`

If we want to remove the denominators, we should multiply both sides by each denominator.

First, let's multiply both sides by C.

`(A)/(C)*C = (B)/(D)*C`

`A = (B)/(D)*C`

Now let's multiply both sides by D.

`A*D = (B)/(D)*C*D`

`A*D = B*C`

So now we removed the denominators.

Now let's do this to our expression.

`2 - (3)/(4*x) = (9)/(10)`

First, let's multiply both sides by 10

`(2 - (3)/(4*x))*10 = (9)/(10)*10`

`20 + (30)/(4*x) = 9`

Now let's multiply both sides by 4*x

`(20 + (30)/(4*x))*4*x = 9*4*x`

`20*4*x - 30 = 9*4*x`

`80*x - 30 = 36*x`

Now we can solve this for x:

`80*x - 36*x = 30`

`44*x = 30`

`x = (30)/(44) = 0.68`