# Solve forx, =>(1− 5 /12)-:(5/6+1/3)=x-:(9/8 − 5/8)?

May 1, 2016

$x = \frac{1}{4}$

#### Explanation:

According to B.E.D.M.A.S., start with the brackets. Within the brackets, if the denominators are not the same, find the L.C.M. (lowest common multiple) between the two denominators and rewrite the fractions.

$\left(1 - \frac{5}{12}\right) \div \left(\frac{5}{6} + \frac{1}{3}\right) = x \div \left(\frac{9}{8} - \frac{5}{8}\right)$

$\left(\frac{12}{12} - \frac{5}{12}\right) \div \left(\frac{5}{6} + \frac{2}{6}\right) = x \div \left(\frac{9}{8} - \frac{5}{8}\right)$

Simplify the brackets.

$\frac{7}{12} \div \frac{7}{6} = x \div \frac{4}{8}$

$\frac{7}{12} \cdot \frac{6}{7} = x \div \frac{4}{8}$

The $7$'s cancel each other out while the $\textcolor{t e a l}{6}$ and $\textcolor{t e a l}{12}$ can be reduced.

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}}{\textcolor{t e a l}{12} \textcolor{b l u e}{\div 6}} \cdot \frac{\textcolor{t e a l}{6} \textcolor{b l u e}{\div 6}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}} = x \div \frac{4}{8}$

$\frac{1}{2} = x \div \frac{4}{8}$

$x = \frac{1}{2} \cdot \frac{4}{8}$

The $\textcolor{p u r p \le}{2}$ and $\textcolor{p u r p \le}{4}$ can be reduced.

$x = \frac{1}{\textcolor{p u r p \le}{2} \textcolor{\mathmr{and} a n \ge}{\div 2}} \cdot \frac{\textcolor{p u r p \le}{4} \textcolor{\mathmr{and} a n \ge}{\div 2}}{8}$

$x = \frac{1}{1} \cdot \frac{2}{8}$

$x = \frac{2}{8}$

$x = \frac{2 \textcolor{red}{\div 2}}{8 \textcolor{red}{\div 2}}$

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{x = \frac{1}{4}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$