Question

1.   |5 - x| - x = 7
2.   |x - 5| + x < 7

x = ?

Answer 1

Aplicam urmatoarea proprietate :

|$x$| = $\left \{ {{x , x \geq 0} \atop {-x,x<0}} \right.$

1. |$5-x$| = $7+x$
Cazul 1 :
$5-x = 7 + x ==> 2x = -2 ==> x = -1$
Cazul 2 :
$5-x = -7-x ==> 5 = -7 ==> Contradictie$

2.
|$x-5$| < $7-x$
Cazul 1 :
$x-5<7-x ==> 2x<12==> x<6$
Cazul 2:
$x-5<-7+x ==> -5<-7 ==> Contradictie$