Question

Arrange the following given equation in descending order of their positive roots

Answer 1

Since, we have to arrange in descending order of roots i.e. $x>0.$
$a)$ For any positive real number $x,$
$|x+2|=4$
Now, using $|a+b|=|a|+|b|\forall ab\ge 0\Rightarrow |x+2|=|x|+2=4\Rightarrow |x|=2\Rightarrow x=2$

$b)$ For any positive real number $x,$
$|5x+7|=37$
Now, using $|a+b|=|a|+|b|\forall ab\ge 0\Rightarrow |5x+7|=|5x|+7=37\Rightarrow |5x|=30\Rightarrow x=6$

$c)$ For any positive real number $x,$
$|2x+3|=9$
Now, using
$|a+b|=|a|+|b|\forall ab\ge 0\Rightarrow |2x+3|=|2x|+3=9\Rightarrow |2x|=6\Rightarrow x=3$

$d)$ For any positive real number $x,$
$|8x+5|=13$
Now, using
$|a+b|=|a|+|b|\forall ab\ge 0\Rightarrow |8x+5|=|8x|+5=13\Rightarrow |8x|=8\Rightarrow x=1$