[ The number of solutions of the equation 2 x+3 x=, x [-2 , 2 ]- ()/(2), (3 )/(2) is: ]

Question

$$
\text { The number of solutions of the equation } 2 x+3 \tan x=\pi, x \in[-2 \pi, 2 \pi]-\left\{ \pm \frac{\pi}{2}, \pm \frac{3 \pi}{2}\right\} \text { is: }
$$

Accepted Answer

$$\begin{aligned}
& 2 x+3 \tan x=\pi \
& \Rightarrow \quad \tan x=\frac{\pi-2 x}{3}, x \in[-2 \pi, 2 \pi]-\left\{ \pm \frac{\pi}{2}, \pm \frac{3 \pi}{2}\right\}
\end{aligned}$$

5 solutions

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