Question

1.Rozwiąż rownanie:

a)|x+4|=14

b)|x-100|=1

c)|x+7|=0,05

d)|10-x|=4

e)|x-⅓|=½

f)|x+0,25|=¾

2.Rozwiaz nierownosc:

a)|x+2|≤3

b)|x-4|=≥4

c)|x+6|>3

d)|8-x|<1

e)|x-5/6|≥½

f)|3-x|≤10/3

g)|0,75+x|≤√1 i 9/16

h)|x+11|>0

h)|x-3|≥-1

Pomocy! daje naj;]

Answer 1

zad.1

a)|x+4|=14

1. Dla x+4 ≥0          2.Dla x+4<0

x≥-4                     x<-4

x+4=14                        -x-4=14

x=10                             x=-18

b)|x-100|=1

1.dla x-100≥0                   2.dla x-100<0

x≥100                                   x<100

x-100=1                            -x+100=1

x=101                                     x=99

c)|x+7|=0,05

1. Dla x+7≥0                     2.dla x+7<0

x≥-7                           x<-7

x+7=0,05                             -x-7=0,05

x=-6,95                                x=-7,05

d)|10-x|=4

1.dla 10-x≥0                2.dla 10-x<0

x≤10                            x>10

10-x=4                              x-10=4

x=6                                  x=14

e)|x-⅓|=½

1.dla x-⅓≥0                     2.dla x-⅓<0

x≥⅓                                 x<⅓

x-⅓=½                            -x+⅓=½

x=⅚                                 x=-⅙

f)|x+0,25|=¾

1.dla x+0,25≥0                    2.dla x+0,25<0

x≥-0,25                               x<-0,25

x+¼=¾                                    -x-¼=¾

x=½                                         x=-1

 

2.Rozwiaz nierownosc:

a)|x+2|≤3

1.dla x+2≥0                  2.dla x+2<0

x≥-2                                x<-2

 

x+2≤3                            -x-2≤3

x≤1                               x≥-5

x nalezy do przedziału <-5,1>

b)|x-4|=≥4

1.dla x-4≥0                      2. dla x-4>0

x≥4                                       x<4

 

x-4≥4                   -               -x+4≥4

x≥8                                      x≤0

x nalezy do przedziału (-∞,0> ∨<8,∞)

c)|x+6|>3

1.dla x+6≥0               2.dla x+6<0

x≥-6                       x<-6

x+6>3                           -x-6>3

x>9                                  x<-9

(-∞,-9>∨ <9,∞)

d)|8-x|<1

1.dla 8-x≥0

x≤8

8-x<1

x>7

2, dla 8-x<0

x>8

-8+x<1

x<9

x nalezy (7,9)

 

e)|x-5/6|≥½

1.dla x-5/6≥0

x≥⅚

x-5/6≥½

x≥1⅓

 

2.x-5/6<0

x<⅚

-x+⅚≥½

x≤⅓

 

f)|3-x|≤10/3

1.dla 3-x ≥0

x≤3

3-x≤3⅓

x≥⅓

2.dla 3-x<0

x>3

-3+x≤3⅓

x≤6⅓

 

g)|0,75+x|≤√1 i 9/16

1.dla ¾+x≥0

x≥-¾

¾+x≤1¾

x≤1

 

2. dla ¾+x<0

x<-¾

-¾-x≤1¾

x ≥1½

 

h)|x-3|≥-1

1. dla x-3≥0

x≥3

x-3≥-1

x≥2

2,dla x-3<0

x<3

-x+3≥0

x≤3