Wiskunde Multiple Choice Vraag

Wat is de oplossingen- verzameling van $\left \| \frac{2x-1}{x+1}\right \|\geqslant 2$ ?	A. ⁻
B. \(]-\infty,-\frac14]\;\backslash\; \{-1\}\)
C.
D. \(]-1,-\frac14\:]\)
E. \(]-\infty,-1\:[\)

$\inline\left | \frac{2x-1}{x+1}\right |\geqslant 2\\ \frac{2x-1}{x+1}\leq-2 \quad \vee \quad \frac{2x-1}{x+1}\geq 2\\ \frac{2x-1}{x+1}+2 \leq 0 \quad \vee \quad \frac{2x-1}{x+1}-2\geq 0\\ \frac{2x-1+2x+2}{x+1}\leq 0 \quad \vee \quad \frac{2x-1-2x-2}{x+1}\geq 0\\ \frac{4x+1}{x+1}\leq 0 \quad \vee \quad \frac{-3}{x+1}\geq 0\\ x \in \:]-1,-\frac14\:]\quad \vee \quad x <-1\\ x\in]-\infty,-\frac14]\;\backslash\;\{-1 \}$