Question

$x+3\left|x\right|=10$. Find the value of $x$.

Answer 1

Solution.

Consider the given equation,

. $x+3\left|x\right|=10$

Case 1: When $x$ is positive.

$$\begin{gathered} \Rightarrow x+3x=10 \\ \Rightarrow 4x=10 \\ \Rightarrow x=\frac{10}{4} \\ \therefore x=\frac{5}{2} \end{gathered}$$

Case 2: When $x$ is negative.

$$\begin{gathered} \Rightarrow x-3x=10 \\ \Rightarrow -2x=10 \\ \Rightarrow x=\frac{-10}{2} \\ \therefore x=-5 \end{gathered}$$

Thus, the value of $x$ are $\frac{5}{2},-5$.