Question #fe19f

Feb 4, 2017

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

Explanation:

The answer to this question is the solution to the equation:

$\frac{4}{5} - x = \frac{2}{3}$

To combine the fractions, first find the least common factor of $3$ and $5$ by looking at the multiples of the largest number, and choosing the first one that is a multiple of the lower one. In our case, that least common factor is $15$. Then, multiply the numerator and denominator of each fraction by the same number, to get equivalent fractions with $15$ in the denominator, then subtract the resulting $\frac{10}{15}$ from both sides:

$\frac{12}{15} - \frac{15 x}{15} - \frac{10}{15} = 0 \implies \frac{12 - 15 x - 10}{15} = 0$

$\implies \frac{2 - 15 x}{15} = 0 \implies 2 - 15 x = 0 \implies 15 x = 2 \implies x = \frac{2}{15}$

Note that when we have a zero on one side, we can multiply both sides of the equation with the denominator to get rid of it, since the zero "absorbs" it ($15 \cdot 0 = 0$)