Given that x < 5, rewrite 8x + 5 - |x - 5| without using absolute value signs.
$8x+5-\sqrt{(x-5)^2}$
The above answer works for all $x$. If we know that $x<5$, we have $8x+5-|x-5|= 8x+5 - (5-x) = 8x+5-5+x= 9x$.
If x<5, then |x−5|<0. |x−5| would be 5−x. So 8x+5−|x−5| would be 9x.
