Question

|2x+1|=11
|3x-2|=7
|4x+8|=0
3-|2x-3|=3
|5x+8| + 9 = 4
3|x-1| +4|x-1|=14
|2x-4| + |3x-6|=10
|3x+3| - 5 = 2|x + 1 |
||x|-3|

Answer 1

a)|2x+1|=11

2x+1=11

-(2x+1)=11

2x=11-1=10

$x = \frac{10}{2} = 5$

-2x-1=11

-2x=11+1=12

$x = - \frac{12}{2} = - 6$

b)|3x-2|=7

3x-2=7

-(3x-2)=7

3x=7+2=9

$x = \frac{9}{3} = 3$

-3x+2=7

-3x=7-2=5

$x = - \frac{5}{3}$

c)|4x+8|=0

4x+8=0

4x=-8

$x = - \frac{8}{4} = - 2$

d)3-|2x-3|=3

-|2x-3|=0

|2x-3|=0

2x-3=0=>2x=3

$x = \frac{3}{2}$

e)|5x+8|+9=4

|5x+8|=4-9=-5

5x+8=-5

-(-5x+8)=-5

5x=-5-8=-13

$x = - \frac{13}{5}$

-5x-8=-5

-5x=-5+8=3

$x = - \frac{3}{5}$

Nu există soluții.

f)3|x-1|+4|x-1|=14

7|x-1|=14

$|x - 1| = \frac{14}{7} = 2$

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}