Find-the-inequality-with-integer-coefficient-for-the-given-solution-set-x-x-lt-2-5-or-gt-2-5-

Question Number 151622 by otchereabdullai@gmail.com last updated on 22/Aug/21

Find the inequality with integer

coefficient for the given solution set

x : x < \frac{- 2}{5} or > \frac{2}{5}

Answered by Rasheed.Sindhi last updated on 22/Aug/21

x < \frac{- 2}{5} or > \frac{2}{5}

5 x < - 2 or 5 x > 2

5 x + 2 < 0 or 5 x - 2 > 0

(5 x + 2) (5 x - 2) < 0

{25 x}^{2} - 4 < 0

Commented by mr W last updated on 22/Aug/21

5 x + 2 < 0 or 5 x - 2 > 0

w h e n 5 x + 2 < 0, t h e n 5 x - 2 < 0

o r

w h e n 5 x - 2 > 0, t h e n 5 x + 2 > 0

i n b o t h c a s e s :

(5 x + 2) (5 x - 2) > 0 n o t < 0

i . e . 25 x^{2} - 4 > 0 n o t < 0

Commented by mr W last updated on 22/Aug/21

\Rightarrow {\begin{cases} x > - \frac{2}{5} & x > \frac{2}{5} \Rightarrow x > \frac{2}{5} \\ OR \Rightarrow o r \\ x < - \frac{2}{5} & x < \frac{2}{5} \Rightarrow x < - \frac{2}{5} \end{cases}

t h i s i s e x a c t l y x < - \frac{2}{5} o r x > \frac{2}{5}

w h i c h i s r e q u e s t e d .

w h y y o u c h a n g e d i t t o

x > - \frac{2}{5} o r x < \frac{2}{4} ?

Commented by otchereabdullai@gmail.com last updated on 22/Aug/21

ok! i now see how to aproach such

questions thanks a lot sir! Rasheed

and Prof W

Commented by Rasheed.Sindhi last updated on 22/Aug/21

m r W s i r

(5 x + 2) (5 x - 2) > 0

\Rightarrow {\begin{cases} 5 x + 2 > 0 & 5 x - 2 > 0 \\ OR \\ 5 x + 2 < 0 & 5 x - 2 < 0 \end{cases}

\Rightarrow {\begin{cases} x > - \frac{2}{5} & x > \frac{2}{5} \\ OR \\ x < - \frac{2}{5} & x < \frac{2}{5} \end{cases}

⇏ x \overset{✓}{<} - \frac{2}{5} o r x < \frac{2}{5}

{W h e r e}^{'} s e r r o r s i r ?

Commented by Rasheed.Sindhi last updated on 22/Aug/21

\underset{\underset{\underset{\underset{\underset{S}{K}}{N}}{A}}{H}}{T} A \underset{\underset{T}{O}}{L} \underset{\underset{\underset{!}{R}}{I}}{S} I c o r r e c t e d m y m i s t a k e .