algebra problems?

Question

1)6x+7=8x-13
2)3n/5-2/5=7/10
3)13.7b-6.5=-2.3b+8.3
4)3/2y-y=4+.5y
5)-7(x-3)=-4
6)28-2.2y=11.6y+262.6
7)7-3x=x-4(2+x)
8)6(y+2)-4=-10
9)-8(4+9x)=7(-2-11x)
10)4(2a-8)=1/7(49a+70)
11)diophantus passed one sixth of his life in childhood, one twelth in youth, and one seventh more as a bachelor. five years after his marriage, there was born a son who died four years before his father, at half his father's (final) age. how old was diophantus when he died.

any answers are helpful, i'm not sure if i've been doing it right.(some are false)

Answer 1

The first 10 problems simply exercise your
algebra mechanics, but the story problem was
more interesting.

So, let "D" represent the number of years in
Diophantus' life. The problem breaks down his
life into several segments:

D = (1/6)D + (1/12)D + (1/7)D + 5 + X + 4

And it also describes the length of the child's
entire life, "C", as being half of "D":

X = (1/2) D

So, solving:

D = (2/12)D + (1/12)D + (1/7)D + 5 + (6/12)D + 4
D = (3/4)D + (1/7)D + 9
D = (21/28)D + (4/28)D + 9
D = (25/28)D + 9
(3/28)D = 9
D = 9(28/3)
D = 3*28
D = 84

childhood = (1/6)84 = 14
youth = (1/12)84 = 7
bachelor = (1/7)84 = 12

Child lived to be 42

14+7+12+5+42+4 = 84

Diophantus died at the age of 84

Answer 2

1)6x+7=8x-13
20 = 2x
10 = x

2)3n/5-2/5=7/10
6n - 4 = 7
6n = 11
n = 11/6

3)13.7b-6.5=-2.3b+8.3
16b = 14.8
b = 14.8/16 = .925

4)3/2y-y=4+.5y
.5y = 4 + .5y
Impossible

5)-7(x-3)=-4
-7x = - 25
x = 25/7

6)28-2.2y=11.6y+262.6
-234.6 = 13.8y
-17 = y

7)7-3x=x-4(2+x)
7 - 3x = -8 - 3x
Impossible

8)6(y+2)-4=-10
6y = -18
y = -3

9)-8(4+9x)=7(-2-11x)
-32 - 72x = -14 - 77x
5x = 18
x = 18/5

10)4(2a-8)=1/7(49a+70)
8a - 32 = 7a + 10
a = 42

11)diophantus passed one sixth of his life in childhood, one twelth in youth, and one seventh more as a bachelor. five years after his marriage, there was born a son who died four years before his father, at half his father's (final) age. how old was diophantus when he died.

84 yrs old
14 years of childhood
7 years of youth
12 years as a bachelor
5 years of marriage (means he was 38 when the son was born)
Son died when father was 38 + .5*84 = 80
80 + 4 = 84 checks

Answer 3

is this your homework?
i'll do numbers 1, 2, 3 with formulas, the others just answers, you practice on the formulas for the others okay? but number 11 is hard sorry...here goes

1)
6x + 7 = 8x - 13
6x - 8x = -13 - 7
-2x = -20...divide both sides by -2
x = 10

2)
3n/5 - 2/5 = 7/10
(3n - 2) / 5 = 7 / 10
(3n - 2) * 10 = 7 * 5
30n - 20 = 35
30n = 35 + 20
30n = 55
n = 55/30 or 11/6

3)
13.7b - 6.5 = -2.3b + 8.3
13.7b + 2.3b = 8.3 +6.5
16b = 14.8
b = .925

4) false
5) x = 25/7 or 3.57
6) y = 234.6/9.4 or 24.957
7) false
8) y = -3
9) x = 18/5 or 3.6
10) a = 42
11) i'm sorry about # 11, i'm running out of patience and my brain got stuck but hope this helps ;-)

Answer 4

2 is 11/6

Answer 5

1) x=10
2) n = 3.5
3) b=14.8/16
4)
5) x = 25/(-7)
6)
7) no solution
8) y=-3
9)

That's the best I can do in my head.