orlovskihmw

2022-07-11

Mixed Fractional Equation?
$3\frac{3}{5}+\frac{2}{x}=4\frac{4}{15}$
I tried subtracting by both sides, etc, but it didn't come out right. I also tried multiplying by both sides, but, it didn't seem to work. what would be the proper way to solve this? Thanks!

trantegisis

Expert

Lets convert the mixed fractions into improper fractions to get the equivalent equation:
$\frac{18}{5}+\frac{2}{x}=\frac{64}{15}$
We now multiply nominator and denominator of the first fraction by three so that both fractions have the same denominator:
$\frac{54}{15}+\frac{2}{x}=\frac{64}{15}$
We now isolate the term $\frac{2}{x}$:
$\frac{2}{x}=\frac{64}{15}-\frac{54}{15}$
We do the fraction substraction:
$\frac{2}{x}=\frac{64-54}{15}=\frac{10}{15}$
We then mutiply by 15 to get:
$\frac{30}{x}=10$
We multiply by x to get:
$30=10x$
Finally we divide by 10 to get: $x=\frac{30}{10}$ which is 3.

Rebecca Villa

Expert

Ok. So I assume you are trying to solve for x. So first we do this:
$\frac{2}{x}=4\frac{4}{15}-\frac{18}{5}=\frac{64}{15}-\frac{54}{15}=\frac{2}{3}$
Then
$2=x\frac{2}{3}\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}x=\frac{2}{\frac{2}{3}}=3$

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