Question

1/4r-1/16r+1/2r=1/2r solve the equation

Answer 1

solve for by simplifying both sides of the equation, then isolation the variable.

r = 0

:)))

Answer 2

The writing is a bit ambiguous, so I'm assuming that the equation is

$\frac{1}{4}r - \frac{1}{16}r + \frac{1}{2}r = \frac{1}{2}r$

Since $\frac{1}{2}r$ appears as an additive term on both sides, you can simplify it, remaining with

$\frac{1}{4}r - \frac{1}{16}r = 0$

Factor the common r:

$(\frac{1}{4} - \frac{1}{16})r = 0$

If a multiplication equals zero, one of the factors equal zero. Since the numeric fraction is not zero, the only option is $r=0$.

I don't believe this is the case, but in case the equation actually was

$\frac{1}{4r} - \frac{1}{16r} + \frac{1}{2r} = \frac{1}{2r}$

proceed as before to get rid of terms appearing on both sides and factor the r (except now it is at the denominator):

$\frac{1}{4r} - \frac{1}{16r} = 0$

$\frac{1}{r}(\frac{1}{4} - \frac{1}{16}) = 0$

Again, one of the factor has to be zero, but none of the factor can equal zero, so the equation has no solutions.