for-what-values-of-x-if-x-x-1-2x-3-gt-0-

Question Number 33836 by NECx last updated on 25/Apr/18

f o r w h a t v a l u e s o f x i f

\frac{x (x - 1)}{2 x + 3} > 0

Answered by Rasheed.Sindhi last updated on 26/Apr/18

\frac{x (x - 1)}{2 x + 3} > 0 {\begin{cases} x (x - 1) > 0 \land 2 x + 3 > 0 \dots A \\ x (x - 1) < 0 \land 2 x + 3 < 0 \dots . B \end{cases}

A : x > 0 \land x - 1 > 0

x > 0 \land x > 1

x > 1

o r

x < 0 \land x - 1 < 0

x < 0 \land x < 1

x < 0

Cont .

Commented by NECx last updated on 26/Apr/18

p l e a s e I d o n t r e a l l y u n d e r s t a n d

t h i s s t y l e . P l e a s e s h e d m o r e

l i g h t o n t h e p r i n c i p l e g o v e r n i n g

t h i s s t y l e . T h a n k y o u s i r

Answered by MJS last updated on 26/Apr/18

2 x + 3 \neq 0 \Rightarrow x \neq - \frac{3}{2}

1 . 2 x + 3 < 0 \Rightarrow x < - \frac{3}{2}

x (x - 1) < 0

1.1 . x < 0 \land x - 1 > 0 \Rightarrow no solution

1.2 . x > 0 but x < - \frac{3}{2} \Rightarrow no solution

2 . 2 x + 3 > 0 \Rightarrow x > - \frac{3}{2}

x (x - 1) > 0

2.1 . x > 0 \land x - 1 > 0 \Rightarrow x > 1

2.2 . x < 0 \land x - 1 < 0 \Rightarrow x < 0

- \frac{3}{2} < x < 0 \lor x > 1

x \in] - \frac{3}{2}; 0 [\cup] 1; \infty [

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