Mixed Fractional Equation?

Question

$$3 \frac{3}{5} + \frac{2}{x} = 4\frac{4}{15}$$

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!

Answer 1

$3\frac{3}{5}=\frac{18}{5}=\frac{54}{15}$

$4\frac{4}{15}=\frac{64}{15}$

Now,

$\frac{2}{x}=\frac{64}{15}-\frac{54}{15}=\frac{10}{15}$

Taking reciprocals,

$\frac{x}{2}=\frac{15}{10}$

$x=\frac{15}{5}=3$

Done.

Answer 2

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 $$2 = x\frac{2}{3} \implies x = \frac{2}{\frac{2}{3}} = 3$$

Answer 3

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 $3$.

Answer 4

First note that $$ \pm k\frac{a}{b}=\pm k\pm \frac{a}{b} $$ So now we have $$3 \frac{3}{5} + \frac{2}{x} = 4\frac{4}{15}$$ $$ \frac{2}{x} = 4\frac{4}{15}- 3 \frac{3}{5} = 4\frac{4}{15}- 3 \frac{9}{15} $$ $$ \frac{2}{x} = 1-\frac{5}{15} = \frac33-\frac{1}{3}=\frac23 $$ Therefore $$ x=3 $$