a)|2x+1|=11
2x+1=11
-(2x+1)=11
2x=11-1=10
[tex]x = \frac{10}{2} = 5 [/tex]
-2x-1=11
-2x=11+1=12
[tex]x = - \frac{12}{2} = - 6[/tex]
b)|3x-2|=7
3x-2=7
-(3x-2)=7
3x=7+2=9
[tex]x = \frac{9}{3} = 3[/tex]
-3x+2=7
-3x=7-2=5
[tex]x = - \frac{5}{3} [/tex]
c)|4x+8|=0
4x+8=0
4x=-8
[tex]x = - \frac{8}{4} = - 2 [/tex]
d)3-|2x-3|=3
-|2x-3|=0
|2x-3|=0
2x-3=0=>2x=3
[tex]x = \frac{3}{2} [/tex]
e)|5x+8|+9=4
|5x+8|=4-9=-5
5x+8=-5
-(-5x+8)=-5
5x=-5-8=-13
[tex]x = - \frac{13}{5} [/tex]
-5x-8=-5
-5x=-5+8=3
[tex]x = - \frac{3}{5} [/tex]
Nu există soluții.
f)3|x-1|+4|x-1|=14
7|x-1|=14
[tex] |x - 1| = \frac{14}{7} = 2[/tex]
x-1=2
-(x-1)=2
x=2+1=3
-x+1=2
1-x=2
-x=2-1=1
x=-1
S={3,-1}
h)|3x+3|-5=2|x+1|
(3x+3)-5=2(x+1)
(3x+3)-5=2×-(x+1)
3x+3-5=2(x+1)
3x-2=2(x+1)
3x-2=2x+2
3x=2x+2+2=2x+4
3x-2x=4
x=4
3x+3-5=2×-(x+1)
3x+3-5=-2(x+1)
3x-2=-2x-2
3x=-2x
3x+2x=0
5x=0
x=0
S={4}
