Question

If the mean of $x+2$, $2x+3$, $3x+4$, and $4x+5$ is $2$, find the value of $x$.

Answer 1

Solve for the required value

Given expressions are, $x+2$, $2x+3$, $3x+4$, and $4x+5$ and their mean is $2$.

The formula for mean is given as,

$\mu =\frac{\sum _i{x}_i}{N}$
where $\mu$ is the mean, $x_i$ is the $i^{th}$ data and $N$ is the total number of values.

Here, $\mu =2$, $N=4$ and $\sum _i{x}_i=\left(x+2\right)+\left(2x+3\right)+\left(3x+4\right)+\left(4x+5\right)$

Thus,

$\begin{array}{cc}& \frac{\left(x+2\right)+\left(2x+3\right)+\left(3x+4\right)+\left(4x+5\right)}{4}=2\\ \Rightarrow & \frac{10x+14}{4}=2\\ \Rightarrow & 10x=-6\\ \Rightarrow & x=-0.6\end{array}$

Hence, the value of $x$ is $-0.6$.