Question

The number of solutions of the equation $\left[x\right]+2\{-x\}=3x$, is

(where [ ] represents the greatest integer function and {x} denotes the fractional part of x)

• A. $1$
• B. $2$
• C. $3$
• D. $0$

Answer 1

The correct option is C $3$

we know that $1-\left\{x\right\}=\{-x\}$

So,

$x-\left\{x\right\}+2\left\{x\right\}+2=3x$

$\left\{x\right\}+2=2x$

$\left\{x\right\}+2=2\left\{x\right\}+2\left[x\right]$

$\left\{x\right\}+2\left[x\right]=2$

hence only one solution