How do you solve \frac{1}{8} - \frac{3}{4} p = - \frac{1}{2}?

Oct 6, 2016

$p = \frac{5}{6}$

Explanation:

Begin by multiplying $\textcolor{b l u e}{\text{All}}$ terms on both sides of the equation by the LCM of 8 , 4 and 2 which is 8.
Doing this will eliminate all fractions from the equation.

$\left({\cancel{8}}^{1} \times \frac{1}{\cancel{8}} ^ 1\right) - \left({\cancel{8}}^{2} \times \frac{3}{\cancel{4}} ^ 1 p\right) = \left({\cancel{8}}^{4} \times - \frac{1}{\cancel{2}} ^ 1\right)$

$\Rightarrow 1 - 6 p = - 4$

subtract 1 from both sides.

$\cancel{1} \cancel{- 1} - 6 p = - 4 - 1$

$\Rightarrow - 6 p = - 5$

To solve for p, divide both sides by - 6.

$\frac{\cancel{- 6} p}{\cancel{- 6}} = \frac{- 5}{- 6}$

$\Rightarrow p = \frac{5}{6} \text{ is the solution}$