Can anyone please explain this simple algebra answer to me?

Question

This is the problem.
Today a boy is twice as old as he was 4 years ago.

Let b = the boy's age today

b = 2 (b - 4 years)
b = 2b - 8 years
b = 8 years

My question is how did 2b-8 become 8?? Shouldn't it have been figured

b = 2b - 8 (move the b to the other side)
2b - b = -8
b = -8


I know I'm wrong and he can't be a negative 8 yrs old but in the equation, isn't negative 8 the right answer and not 8?

To tgypoi - I don't have a teacher yet. I'm starting college in the fall after being out of school for 30 years! I'm trying to give myself a crash course this summer on algebra basics. That's why I keep asking these stupid questions because I have no one to teach me but a library book and the computer.

Thanks everyone for your answers.

Answer 1

let
b be the boy's age today
so 4 years ago he was b - 4

Today a boy is twice as old as he was 4 years ago.
b = 2(b-4)
b = 2b - 8
b = 8

========================
negative 8 is not the right answer. when you moved 2b to the other side it should have been preceded by a minus sign. adding it to the original term on the left hand side (b)

the resulting equation should have been

-2b + b = -8
-b = -8
b = 8

Answer 2

Let's try and find the mistake. I know how difficult this can be when you've been staring at something for ages.

b = 2b – 8
2b – b = –8 ... oops!

Going through it more slowly ...

b = 2b – 8
b – 2b = –8 ... I've taken the 2b to the left-hand side
–b = –8 ... done the subtraction on the left
b = 8 ... and changed the sign of both sides.

In writing 2b – b = –8 you were doing too many steps at once and confused yourself about the signs.

Answer 3

Let us do it from the basics:

If b is the age of the boy today,

b = 2 (b - 4)

b = 2b - 8

b - 2b = - 8 or - b = -8 and thus b = 8

Alternatively,

2b - b = - (- 8) = + 8

thus b = + 8

What you did wrong was to take the b to the rhs (right hand side) and not taking the - 8 to the lhs, so your equation was set up wrongly.

Answer 4

You have a small mistake here. When you move the 2b on the other side you have to change the sign for 2b NOT for the b. So correctly will be:
b=2b-8
b-2b=-8
-b=-8
b=8

Answer 5

Do the steps systematically and carefully,

From,

b = 2b - 8

First, add (8) to both sides,

b + (8) = 2b - 8 + (8)

b + 8 = 2b

Next,

Subtract (b) from both sides,

b + 8 - (b) = 2b - (b)

8 = b

i.e. b = 8

Answer 6

Age today = b years
4 years ago his age was (b - 4) years
But b = 2 x (b - 4):-
b = 2b - 8
b + 8 = 2b
8 = b
Boy is 8 years of age.
4 years ago he was 4 years of age.

Answer 7

no its not b=2b-8
its2b - 8 = 8
2b = 8 + 8
b = 16/2
b= 8

Answer 8

Your teacher told you to move all the like terms to the same side didn't he? Naughty teacher! You can't just move numbers about to suit yourself. Tell him off next time you see him. (Or her, whatever.)

From b=2b-8
What we do is subtract 2b from both sides;
b-2b=2b-8-2b
On the right hand side, this eliminates the 2b and leaves us with: -b=-8
Now we multiply both sides by -1 and get:
b=8
:)

Answer 9

Hey u r wrong.

b=2b-8
or b-2b+8=0
-b+8=0
Now we get b=8
Just check u didnt change the sign of 8 when u took it to the other side.

Answer 10

alright, you do have to do 3/4-1/2 first. the common denominator is 4, so you change the 1/2 to 2/4 (they're the same thing, but it's easier to subtract 2/4 from 3/4). so, 3/4-2/4--this is easy--is 1/4. after that, you're suppose to multiply the answer by a half. remember "please excuse my dear aunt sally?" (parenthesis, exponents, multiply, divide, add, then subtract) you're suppose to multiply before you add or subtract. so you don't do 2/3-1/2 before you multiply. so, 1/2(1/4) is 1/8 b/c you multiply the numerators together and the denominators together. so, now you do the 2/3-1/8 because it's in parenthesis. the common denominator is 24 because that's the smallest number that both 3 and 8 can evenly divide into. so, you change 2/3 to 16/24 because you have to multiply 3 by 8 to get 24 and you have to multiply the numerator by 8 too to get a fraction that's equal to 2/3. you multiply the top and bottom numbers of 1/8 to get 3/24. Now you have 16/24-3/24 which is 13/24. multiply the top by -3 and the bottom by 5 and get -39/120.