# Given a set  {4,-2,-12,5,x} , for what x would the mean of the set be -5?

Dec 17, 2015

$\textcolor{w h i t e}{\times} - 262$

#### Explanation:

$\textcolor{w h i t e}{\times} \overline{a} = \frac{1}{n} {\sum}_{i = 1}^{n} {a}_{i}$ (the mean of a set of n data points)

$\textcolor{w h i t e}{\times} - 5 = \frac{1}{5} {\sum}_{i = 1}^{5} {a}_{i}$
$\implies \frac{x - 12 - 2 + 4 + 5}{5} = - 5$

Multiply both sides by $5$
$\textcolor{w h i t e}{\times} \textcolor{red}{5 \cdot} \frac{x - 12 - 2 + 4 + 5}{5} = \textcolor{red}{5 \cdot} \left(- 5\right)$
$\implies x - 5 = - 25$

Add $\textcolor{red}{5}$ to both sides
$\textcolor{w h i t e}{\times} x - 5 \textcolor{red}{+ 5} = - 25 \textcolor{red}{+ 5}$
$\implies x = - 20$