Odpowiedzi

2009-11-05T19:07:05+01:00
A. Ιx+1Ι/2=3

Ιx+1Ι=6
x+1=6 v x+1=-6
x=5 v x=-7

b. 6-Ι10-4tΙ=2
Ι10-4tΙ=4
10-4t=4 v 10-4t=-4
-4t=-6 v -4t=-14
t=3/2 v t= 3,5

c. Ι4z+1Ι>5
4z+1>5 v 4z+1<-5
4z>4 v 4z<-6
z>1 v z<-1,5

d. Ι3y+5Ι≤4
3y+5≤4 ∧ 3y+5≥-4
3y≤-1 ∧3y≥-9
y≤-1/3 ∧y≥-3
y∈<-3,-1/3>
2009-11-05T19:07:13+01:00
A. Ιx+1Ι/2=3
|x+1|/2=3 /*2
|x+1|=6/-1
|x|=5
x=5

b. 6-Ι10-4tΙ=2 /+|10-4t|
6= 2+ |10-4t| /-2
4= |10-4t| \-10
-6= |-4t| \:-4
1,5= |t|
t= 1,5
c. Ι4z+1Ι>5
|4z+1|>5//-1
|4z|>4 /:4
|z|>1
z>1
d. Ι3y+5Ι≤4
|3y+5|≤4 /-5
|3y|≤ -1 /:3
|y|≤ -1/3
y≤1/3
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2009-11-05T19:10:39+01:00
A) |x+1| / 2 = 3
|x+1| / 2 = 3 /*2
|x+1| = 6
x + 1 = 6 v x + 1 = -6
x = 5 v x = -7

b) 6 - 10-4t = 2 ∨ 6 - 10-4t = -2
-4t = 6 ∨ -4t = 2
t = 1,5 ∨t = 0,5

c) 4z + 1 > 5 ∨ 4z + 1 < -5
4z > 4 ∨ 4z < -6
z = > 1 ∨ z < -6/4

d) 3y + 5 ≤ 4 ∧ 3y + 5 ≥ -4
y ≤ -1/3 ∧ y ≥ -3