Question

Rezolvati in Z ecuatiile
a)|x|=7
b)|x|=23
c)|x|=0
d)|5x-3|=2
e)|x|=-4
f)|4x|=16
g)|x+5|=7

Answer 1

a. x=7 sau -7
b.x=23 sau -23
c.x=0
d.I 5x-3=2
5x=5
x=1
II 5x-3=-2
5x=1
x=1/5
e. nu se poate, modulul unui numar nu poate fi un numar negativ
f.4x=16 sau -16
x=4 sau -4
g.I x+5=7
x=2
II x+5=-7
x=-12

Answer 2

$a).|x|=7 \\ x=-7;x=7 \\ b).|x|=23 \\ x=-23;x=23 \\ c).|x|=0 \\ x=0 \\ d).|5x-3|=2 \\ 5x-3=2 \\ 5x=2+3 \\ 5x=5 \\ x=1 \\ 5x-3=-2 \\ 5x=-2+3 \\ 5x=1 \\ x= \frac{1}{5} \\ x=1;x= \frac{1}{5}$
$e).|x|=-4 (Fals) \\ f).|4x|=16 \\ 4x=16 \\ x=4 \\ 4x=-16 \\ x=-4 \\ x=-4;x=4$
$g).|x+5|=7 \\ x+5=7 \\ x=7-5 \\ x=2 \\ x+5=-7 \\ x=-7-5 \\ x=-12 \\ x=-12;x=2$