how to solve linear equations?

Question

its been a while since I have done any of these...and i cannot remember how to do them...can someone please explain to me how to?

if an example is needed, here is one- 5a+12=6-3a

thanks =)

Answer 1

group all terms that you can add/subtract on one side of the equation, then put everything else on the other side. after that, you can then solve for a by dividing both sides of the equation by whatever number is written next to a.

Answer 2

Remember to do everything on both sides.

5a + 12 = 6 - 3a
5a + 12 + 3a = 6 - 3a + 3a
(5a + 3a) + 12 = 6 (- 3a + 3a)
8a + 12 = 6
8a + 12 - 12 = 6 - 12
8a = -6
8a * 1/8 = -6 * 1/8
a = -6/8 = -3/4

You can check this:

(5 * -3/4) + 12 = 6 - (3 * -3/4)

-15/4 + 12 = 6 - -9/4

-3-3/4 + 12 = 6 + 2-1/4

8-1/4 = 8-1/4

Answer 3

5a+12=6-3a
next, transpose 3a to the other side of the equation by adding 3a to both sides
5a+3a+12=6-3a+3a which eliminates 3a from thew right side
Then transpose 12 to the right side of the equation by subtracting 12 from both sides
5a+3a+12-12=6-12 which eliminates 12 in the left side.
then combine like terms (add 5a and 3a, subtract 12 from 6)
which would equal to 8a=-6
you need to find a, so divide both side by 8 to isolate the a
so a=-6/8 or a=-3/4

Answer 4

Get all the variables on one side and the constants one the other side of the equal sign

5a+3a=6-12
(remember to change the symbols when shifting the constants and the variables to the other side of the equal sign)

8a=-6
a=-6/8
a=-3/4 (simplify the fraction -6/8)

Answer 5

get all the variables on the same side of the equal sign, and everything else on the other... so we do this

5a + 12 = 6 - 3a

we need to gather up all the a's, so let's add 3a to both sides first.

8a + 12 = 6

gotta get rid of the 12 and 8... 12 first (subtracting)

8a = -6

and now divide by 8

a = -6/8

a = -3/4

Answer 6

you isolate the wariabels on one side.
-5a+12=6-3a
-5a+5a+12-6=6-6-3a+5a
6=2a
6/2=2a/2
3=a