Vì | x + $\frac{1}{101}$ | + | x + $\frac{2}{101}$ | + | x + $\frac{3}{101}$ | + ... + | x + $\frac{100}{101}$ | >0

⇒ 101x > 0

⇒ x > 0

⇒ | x + $\frac{1}{101}$ | + | x + $\frac{2}{101}$ | + | x + $\frac{3}{101}$ | + ... + | x + $\frac{100}{101}$ | = x + $\frac{1}{101}$ + x + $\frac{2}{101}$ + x + $\frac{3}{101}$ + ... + x + $\frac{100}{101}$ = 101x

( x + x + x + ... + x ) + ( $\frac{1}{101}$ + $\frac{2}{101}$ + $\frac{3}{101}$ + ... + $\frac{100}{101}$ ) = 101x

100x + ( $\frac{1}{101}$ + $\frac{2}{101}$ + $\frac{3}{101}$ + ... + $\frac{100}{101}$ ) = 101x

$\frac{1}{101}$ + $\frac{2}{101}$ + $\frac{3}{101}$ + ... + $\frac{100}{101}$  = x

$\frac{1+2+3+...+100}{101}$ = x

Đặt A = 1+2+3+...+100

A= (100+1)×100÷2= 5050

⇒ $\frac{5050}{101}$ = x

x= 50

Vậy x=50