Question

-5 < x -4 < 9 - 2x and x is a perfect square then find the value of x and represent it on a number line.... god for sake solve this everyone

Answer 1

Answer:

First just split this inequality in two parts

First

$- 5 < x - 4 \\ x > - 5 + 4 \\ x > - 1$

Second

$x - 4 < 9 - 2x \\ x + 2x < 9 + 4 \\ 3x < 13 \\ \\ x < \frac{13}{3}$

So

$x \in \: ( - 1 \: \: \: \: \frac{13}{3})$

Perfect square integers in this interval are

$\{0 \: \: 1 \: \: 4 \}$