Mate

1. HALLAR “x” EN:
4x+60-3x+16x=100+16x-3x
4x-3x+16x-16x+3x=100-60
4x=40
x=40/4
x=10
2. HALLAR “x”, “y” EN:
X+2y=20… (1)X-2y=10... (2)
______
2x =30
x=30/2
x=15

Reemplazando En (1) ≤ ≥
X+2y=20
15+2y=20
2y=20-15
Y=5/2

3. SI A= {x ∈ /R -2<x ≤ 4}B= {x ∈ /R -1≤x <5}
C=<-3,10]

HALLAR Y GRAFICAR

(AUC) ∩ B

4
4
-2
-2
10
10
5
5

-1
-1
-3
-3

RSPT: (AUC) ∩ B = [-1,4]

(BUC)-A

4
4
-2-2
10
10
5
5

-1
-1
-3
-3

RSPT (BUC)-A = <-3,-2] U <4, 10]
4. HALLAR CS; DE:
a) (X+7) (x-2) ≥0
Y EL CS2 DE:
b) x+6 ≤0
X-3

HALLAR: CS1, ∩ CS2

DESARROLLO “A”:a) -
-
+
+
+
+
(X+7) (x-2) ≥0

2
2
-7
-7
X+7=0 x-2=0
X= -7 x=2
RSPT CS1 = <-∞, -7] U [2, +∞>
RSPT CS1= <-∞, -7] U [2, +∞>

PC= {x ∈ -7,2}
DESARROLLO “B”:
b) x+6 ≤0
+
+
-
-
X-3
+
+

-6
-6
3
3
X+6=0 x-3=0
RSPT CS2 = [-6,3>
RSPT CS2 = [-6, 3>
X=-6 x=3
PC= {x ∈-6,3}

RSPT CS2 = [-6, 3>
RSPT CS2 = [-6, 3>
RSPT CS1 = <-∞, -7] U [2, +∞>
RSPT CS1 =<-∞, -7] U [2, +∞>

3
3
2
2
-6
-6
-7
-7

CS1, ∩ CS2 RSPT= [-6,2]

5. (x+2) (x-7)(x+13)<0
X-14

X+2=0 X-7=0 X+13=0 X-14=0
X=-2 X= 7X= -13 X=14

+
+
-
-
+
+
-
-
+
+

-13
-13
3
3
3
3
3
3



RSPT = <-13,-2> U <7,14>

6. SEA:

M= <-5,8]
N=<-6,7>

HALLAR M-N; MUN;M∩N

M
M

N
N

-6
-6
-5
-5
8
8
7
7

RSPT: M-N= <7,8>
RSPT: MUN= [-6,8>
RSPT: M∩N = [-5,7]

7. SEA: A= {x ∈ /R -1 < x <7}
B=<-3,6]...