# How do you solve -70= - 2p + 4( - \frac { 19} { 6} p - \frac { 17} { 6} )?

Oct 11, 2017

$p = 4$

#### Explanation:

$- 70 = - 2 p + 4 \left(- \frac{19}{6} p - \frac{17}{6}\right)$

Solving the bracket first!

$- 70 = - 2 p + {\cancel{4}}^{2} \left(- \frac{19}{\cancel{6}} _ 3 p - \frac{17}{\cancel{6}} _ 3\right)$

$- 70 = - 2 p + 2 \left(- \frac{19}{3} p - \frac{17}{3}\right)$

$- 70 = - 2 p - \frac{38}{3} p - \frac{34}{3}$

Multiply through with their LCM

$- \frac{70}{1} = - 2 \frac{p}{1} - \frac{38}{3} p - \frac{34}{3}$

LCM = 3

$3 \left(- \frac{70}{1}\right) = 3 \left(- 2 \frac{p}{1}\right) - \cancel{3} \left(\frac{38}{\cancel{3}} p\right) - \cancel{3} \left(\frac{34}{\cancel{3}}\right)$

$3 \left(- 70\right) = 3 \left(- 2 p\right) - 38 p - 34$

Simplifying..

$- 210 = - 6 p - 38 p - 34$

$- 210 = - 44 p - 34$

Collect like terms..

$- 210 + 34 = - 44 p$

$- 176 = - 44 p$

Divide both sides by $\textcolor{red}{- 44}$

$- \frac{176}{\textcolor{red}{- 44}} = \frac{- 44 p}{\textcolor{red}{- 44}}$

${\cancel{- 176}}^{4} / {\cancel{- 44}}_{1} = \frac{\cancel{- 44 p}}{\cancel{- 44}}$

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

$\Rightarrow p = 4$