Răspuns :
|7x+2|-6=4
|7x+2|=4+6
|7x+2|=10
1. 7x+2= -10
7x= -10-2
7x= -12
x= -12/7
2. 7x+2=10
7x=10-2
7x=8
x=8/7
x∈{-12/7,8/7}
|7x+2| - 6 = 4
|7x+2| = 4 + 6 = 10
|7x+2| este egal cu:
[tex] = > 7x + 2 \: dacă \: 7x + 2 \geqslant 0[/tex]
[tex] = > - 7x - 2 \: dacă \: 7x + 2 < 0[/tex]
Cazul 1: 7x+2 >= 0
[tex]=> x \geqslant \frac{ - 2}{7} [/tex]
7x+2 = 10
7x = 10 - 2 = 8
[tex]x = \frac{8}{7} \geqslant - \frac{2}{7} (adevărat)[/tex]
.
Cazul 2: 7x+2 < 0
[tex]=> x < \frac{ - 2}{7} [/tex]
-7x - 2 = 10
-7x = 10 + 2 = 12
[tex]x = - \frac{12}{7} < - \frac{2}{7} (adevărat)[/tex]