linear equation 5a+11=a-13

- anonymous

linear equation 5a+11=a-13

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- anonymous

@LegendarySadist @peachpi

- anonymous

So are we solving for a then?

- anonymous

yes why do people keep saying that??

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## More answers

- anonymous

Well it's always good to confirm what the OP is asking for. There are a lot of people on this site who ask their questions in a confusing way so I've just come to confirm at the start rather than later on lol

- anonymous

kk

- anonymous

Anyways, the way to go about solving this one would be to get all of the a values on one side and all of the number values on the other side.

- anonymous

5a+a first right

- anonymous

Well a is already positive on the right side, so to bring it over we would subtract it.

- anonymous

In other words 5a-a

- phi

you might think like this:
how do I *get rid of a on the right side* ?
answer: add -a
but to keep things equal, you also add -a to the left side.

- phi

ok but not just 4. it is 5 a's take away 1 a.

- anonymous

open study whenever i get on its always acting wierd

- anonymous

6a

- phi

start over, and to it carefully
5a+11=a-13
add -a to both sides. what do you get? (and write out the whole equation)

- anonymous

hold on one sec i need to draw it and it wont let me i'm going to refresh the page.

- anonymous

|dw:1439758244788:dw|

- phi

ok, except a+a is not 0 (it is 2a)
try adding -a to both sides

- anonymous

7a then.

- phi

start over,
5a+11=a-13
add -a to both sides. Just write -a on both sides. can you do that ?

- anonymous

can you show me the steps to the answer i already know the answer its -6

- anonymous

of how you would you do it

- phi

yes, we will get the answer.
I would add -a to both sides. that means write -a on both sides
can you try to do that ?

- anonymous

can you show me in drawing of how the step would be?

- phi

you write -a on both sides , like this
5a+11 -a =a-13 - a

- phi

if we look just at the "a" part , on the right side you have 1a take away 1 a
on the left side you have 5 a's take away 1 a

- anonymous

so its 4a?

- phi

can you write out the whole equation?
start with
5a+11 -a =a-13 - a
and simplify both sides. can you do that ?

- anonymous

yea sure one sec.

- anonymous

5a+-a=a-13a ? is that what i would do on the right side

- phi

you start with
5a+11 -a =a+ -13 + -a
you can switch the order of the right side (if you want) to
5a+11 -a =a+ -a + -13
what is a+ -a ?

- anonymous

2a?

- phi

what is
1+ -1 ?

- anonymous

0

- phi

and 2+ -2
or
3+ -3
or a+ -a
always adds up to 0

- anonymous

kk

- phi

5a+11 -a =a+ -a + -13
the right side, a+ -a is 0
so you get
5a + 11 -a = 0 + -13
0 + -13 is -13 , right?

- anonymous

yes

- phi

so far we figured out
5a + 11 -a = -13
now look at the left side. it says 5 a's and 11 and take away 1 a
we can simplify 5 a's take away 1 a.

- anonymous

4a

- anonymous

no sorry 6a

- phi

ok, but try to get in the habit of writing the whole equation
5 a's take away 1 a is 4 a"s (we write it 4a)
what is the whole equation?

- anonymous

so it is 4a?

- phi

yes. if you had 5 cows and took away 1 cow, how many cows would you have?
it works the same for a's

- anonymous

4a+11=-13

- phi

notice if you could make the 11 "go away" you would have 4a by itself
luckily we can make 11 go away. we add -11
and we have to add -11 to the other side to keep things equal
write -11 on both sides.

- anonymous

then subtract 11to both sides 24 so then it would be 4a=-24

- phi

yes. if we do it this way:
4a+11+-11=-13+-11
then on the left we have 11+-11 which is 0 (just like a+-a is zero)
and on the right side -13 + -11 is -24
so you have
4a = -24
the last step is to divide both sides by 4
\[ \frac{4a}{4} = \frac{-24}{4} \]

- phi

it might not be obvious , by 4a/4 is just a

- anonymous

-6 thanks

- anonymous

a=-6

- phi

yes.
good job.
if you do a bunch of these problems, it will start to make sense.

- anonymous

thanks again. :)

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