solve-4-3-x-lt-8-

Question Number 115035 by bobhans last updated on 23/Sep/20

s o l v e ∣ 4 - \frac{3}{x} ∣ < 8

Commented by bemath last updated on 23/Sep/20

\Leftrightarrow - 8 < 4 - \frac{3}{x} < 8

c a s e (1) \to - 8 < 4 - \frac{3}{x}

\frac{3}{x} < 12; \frac{1}{x} < 4; \frac{1 - 4 x}{x} < 0

\frac{4 x - 1}{x} > 0; x < 0 \cup x > \frac{1}{4}

c a s e (2) 4 - \frac{3}{x} < 8; - \frac{3}{x} < 4

\frac{3}{x} > - 4; \frac{3 + 4 x}{x} > 0

x < - \frac{3}{4} \cup x > 0

s o l u t i o n s e t i s (- \infty, - \frac{3}{4}) \cup (\frac{1}{4}, \infty)

Commented by bobhans last updated on 23/Sep/20

s a n t u y y

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