Question

1/2a+2/3=-1/2a-3/4 solve the following equation.

Answer 1

add 1/2 a to both sides

Answer 2

do you want the answer or a way to solve it?

Answer 3

both would supply.

Answer 4

1/2a+2/3=-1/2a-3/4

if you added "1/2 a" left and right, what do you get ?

Answer 5

1/2a+1/2a+2/3=-3/4

Answer 6

correct

you can combine the "a terms":
\[\frac{ 1 }{ 2 }a+\frac{ 1 }{ 2 }a=a\]

Answer 7

a+2/3=-3/4

Answer 8

yes. now all that remains is to move 2/3 to the other side

because the fractions do not have the same denominator, it is necessary to find a common denominator. it is best to find the least common factor

Answer 9

\[a = -\frac{3}{4}-\frac{ 2 }{ 3 }\]

Answer 10

so the answer it a=-3/2-2/3 ?

Answer 11

*-3/4

Answer 12

you can still simplify the right hand side

-3/2 and -2/3 are both numerical terms, so it's possible to combine them.

Answer 13

-3/4*

Answer 14

\[\frac{ 1 }{ 2 } + \frac{2}{4}=\]it is possible to add fractions if you get them to the same denominator first

Answer 15

:O

Answer 16

extending or reducing fraction changes the denominator, without changing the value

Answer 17

you can solve it that way...with fractions
OR
this way, without fractions...

1/2a + 2/3 = -1/2a - 3/4 (multiply the entire equation by the LCD, which is 12.

12(1/2)a + 12(2/3) = 12(-1/2)a - 12(3/4)
6a + 8 = -6a - 9 (add 6a to both sides)
6a + 6a + 8 = -9 (subtract 8 from both sides)
6a + 6a = -9 - 8 (combine like terms)
12a = - 17 (divide by 12)
a = -17/12 or - 1 5/12

either way you choose to do it, the answers will be the same :)

Answer 18

\[\frac{ 2 }{ 3 } =\frac{ 4 }{ 6 } \]\[=\frac{ 8 }{ 12 }\]

Answer 19

now im confused.. which one is correct?

Answer 20

both are correct. texaschic ones avoids dealing with fractions

Answer 21

but which is in simplified form?

Answer 22

we were left here:
\[a = -\frac{3}{4}-\frac{ 2 }{ 3 }\]

Answer 23

texaschic how did you find the LCD = 12?

Answer 24

which gets the same end result:
\[a = -\frac{9}{12}-\frac{ 8 }{ 12 }= -\frac{ 17 }{ 12 }\]

Answer 25

either way you choose to do the problem, the end result is the same

Answer 26

woah. woah.. so a=-2/3-3/4 is a=−9/12−8/12=−17/12?

Answer 27

correct....when adding/subtracting fractions, they have to have the same denominator.

Answer 28

if hey don't, you have to make them by finding the LCD of the fractions

Answer 29

typo * they

Answer 30

LCD.. how did they become this way? a=−9/12−8/12

Answer 31

ok...let me try to explain...
-2/3 - 3/4 cannot be added together because they have different denominators (bottom numbers).
So we have to make them the same.
We have to find what number 3 and 4 both go into evenly. That would be 12.
So we are going to make 12 the denominator.

-2/3.....how many times does 3 go into 12 ? It goes in there 4 times, then take the 4 and multiply it by the numerator (2). That means 4 x 2 = 8. Put the 8 over the new denominator 12 giving us -8/12.
-3/4....how many times does 4 go into 12 ? It goes in there 3 times. Now multiply 3 by the numerator (3) and you get 9. Put the 9 over the new denominator 12 giving us -9/12.

Now we have : -8/12 - 9/12 (same denominator so we can add).
-8/12 - 9/12 = -17/12

Understand ?

Answer 32

omg xD you explain way better than our professor.. :"> thanks madam..

Answer 33

anytime...glad I could help :)