1. a. 4x-1=2x+7 d. –(2n-
4x-2x=7+1 1)+6(n+3)= -4-(7n-11)
2x=8 -2n+1+6n+18= -4-7n+11
X=8/2 -2n+6n+7n= -4+11-1-18
X=4 11n= -12
n= -12/11
b. 5(2x+1)=4( n= 1,09
3x-7)
10x+5=12x-28 e. 6x2-5x-
10x-12x= -28-5 21=0
-2x= -33
X= -33/-2 X_ -(-5)± √(-5)2-4.6.-21
X= 16,5 ¯ 2.6
c. 3(x-4)- X_ 5± √25+504
7(x+2)= -2(x+18) ¯ 12
3x-12-7x-14= -2x-36
3x-7x+2x= -36+12+14 X_ 5± √529
-2x= -10 ¯ 12
X= -10/-2
X= 5 X_ 5± 23
¯ 12

2. X1_ 5-23 ¯ 2
¯ 12 X1_ 6,25
¯ 2
X1_ 18 X1= 3,1
¯ 12
X2_ 2+8,25
X1= 1,5 ¯ 2
X2_ 5+23 X2_ 10,25
¯ 12 ¯ 2
X2_ 28 X2= 2,33 X2= 5,125
¯ 12
h. √3x+6=x →
2 2 2
f. 16x - √3x=x-6 → 3x=x -6
8x+1=0
x2-3x-36=0
2
X_ -(-8)± √(-8) -4.16.1
¯ 2.16 X_ -(-3)± √(-3)2-4.1.-36
¯ 2.1
X_ 8± √64-64
¯ 32 X_ 3± √9+144
¯ 2
X_ 8± √0
¯ 32 X_ 3± √153
¯ 2
X_ 8
¯ 32 X_ 3± 12,37
¯ 2
X= 0,25
X1_ 3-12,37
g. √2x=x-4 ¯ 2
→ 2x=x2-42
X1_ 9,37
2
x -2x-16=0 ¯ 2
X_ -(-2)± √(-2)2-4.1.-16 X1= 4,68
¯ 2.1
X2_ 3+12,37
X_ 2± √4+64 ¯ 2
¯ 2
X_ 2± √68 X2_ 15,37
¯ 2 ¯ 2
X_ 2± 8,25
¯ 2 X2= 7,68
X1_ 2-8,25

3. a. Tenemos:
Una alcoba = x 6z-20+3z-10+z=230
Dos alcobas = y 6z+3z+z=230+20+10
Tres alcobas= z 10z=260
230 = x+y+z z=260/10
2(3z-10)+3z-10+z=230 z=26
x=2y y=3z-10 z=26
x=2(3z-10) → x=2(3.26-10) → x=2(78-10)
x=2(68) → x=136
y=3z-10 → y=3(26)-10 → y=78-10 → y=68
x+y+z=230 → 136+68+26=230
b. h2=x2+y2 → 52= x2+y2 → x=y → 52= x2+x2
52= 2x2 → 2x2=52 → x2=52 /2 → √x2=√52 /2
x=√52 /2 → x=√25/2 → x=√12,5
x=3,53
y2=h2-x2 → y2=52-3,532 → y=√52-3,532 → y=√25-12,46
y=√12,5
y=3,53