Question

TUTORIAL:

Solving equations.

Answer 1

Please note that I've been getting this request and it's been blowing up my inbox. I am also on a hangover currently.

Answer 2

Allow me to introduce myself, I am a Ph.D graduate and full time professor. Solving equations is really simply. All you have to do is remember a few things.

Rule 1. Do the opposite when solving an equation.
Rule 2. Solve for the variable last. (The variable is the letter.)
Rule 3. What you do too one side, do to the other.

So lets start...

If I had something like:
2 + 2x = 10, can you find the variable? Yes! The variable is the, "x." because it is the letter in the equation.

So now that we found our letter, what do you we now? Well, as the rules state we do the opposite.


So we have the equation:
2 + (2x) = 10. The parenthesis say that we're going to do that part last, because you always solve for your variable last.

What do we mean by doing the opposite? Well you see that, "2," in the equation? Well it's positive, right? It's positive two! So we are going to do the opposite and subtract 2.

The equation now looks like this:

-2 + 2 + 2x = 10 <--- This looks nasty.

However, you see the we have negative two + positive two, which just equals 0. So we are now left with
0 + 2x = 10


And this is equal too:
2x = 10(This is because 0 has no value and is useless.)

Now you HAVE to subtract two from the other side of the equation to maintain equality. You do this for all equations.

Example:
2 + 1x = 3
(-2 )+ 2 + 1x = 3 (- 2)
----------------------
1 + 1x = 2
(-1) + 1 + 2x = 2(-1)
----------------------

You can see that what we do too one side of the equation we must do to the other. It is how we maintain equality. Imagine a scale, and both sides are equal. If I take five pounds of the left side, than the scale is unequal. In order to maintain quality we have too take five pounds off the other side of the scale. That is why we call it an "equation" because both sides must be equal to each other. So after you do the opposite one one side, you must take that number and do the same thing to the other side.


Now the only term remaining is our variable. You can see that our variable is right next to a number. When you have something like 4x, 2x, 1x, etc, etc, etc.. All that is saying is, "Four times x," "Two times x," "One times x," etc.

So we have:
2x = 10 - 2 (Ten minus two is eight.)
2x = 8

Now that we know it is being multiplied, we have to do the opposite until only the variable is remaining. What is the opposite of multiplication? That's right! Division! So we divide 2 by itself and get 1 because 2 can go into itself once!

2
- = 1
2

Now we must also divide the other side of the equation by 2!

1x = 10
--
2

10 can go into 2 how many times? That's right! five times!

We now have:
1x = 5 <--- Correct!

Here are some example problems and tips.

Tips:
The opposite of addition is subtraction
The opposite of subtraction is addition
The opposite of division is multiplication
The opposite of multiplication is division.

Example Problems:
2x + 5 = 27

implies: 2x + = 27 − 5 = 22
(We subtracted five from itself and got 0, then we did the same thing to the other side of t equation and got 22 because 27 - 5 = 22)

I
mplies: 2x = 22 (Two can go into itself once, and into 22 11 times.)
-- --
2 2




implies: 1x = 11.



Example:
Solve for x :
5 − 2x = −11

−2x = −11 − 5 (A minus, minus a minus = a positive.) {That is -11 -5}

2x = 16

x = 8

Answer 3

I appreciate your dedication @Compassionate , way to go.

Answer 4

yes

Answer 5

but finally,u didn't solve the 1st equation,to get x=4....

Answer 6

or u took 10 instead of 8 to get x=5??

Answer 7

seems theres a little mistake

Answer 8

Yes........ 2x + 2 = 10 =========> x = 5 according to u

Answer 9

@Compassionate correct it........ u did 10/2 instead of 8/2

Answer 10

I have a point @Compassionate the way in which u solved the first question is not gud according to me...........
writing 2x = 10 and then saying we will have to do the same for RHS will make the students get confused. They will solve this equation as u did which is WRONG

Answer 11

its a good tutorial just 2 lines need to be removed and itll be fine

Answer 12

Yes,............. Its really wonderful effort on your part but just needs a small correction

Answer 13

I'm so sorry. You guys don't know how tired I am right now...

Answer 14

Np ............ but still great efforts

Answer 15

how dare you correct a PhD graduate and a full-time professor @vishweshshrimali5 lol

Answer 16

lol

even when I am a mere student....... of class 11 ;D

Answer 17

Lol. lgb, stop it. Lol. Go easy on me I'm not feeling good today.

Answer 18

I have a small doubt..

variable is a letter? can it be better explained?

Answer 19

I know that you are tired so no problem take rest for some time and then answer to my quest.

Answer 20

Yes, it can. This is basic though. I'd rather not go into more complex types of variables.

Answer 21

Yes, variable is any quantity which doesn't have any fixed value and changes its value according to a predefined equation

Answer 22

there are many constants that are denoted by letters..

Don't need to go complex @Compassionate The main thing i wanted to mention that is already mentioned by vishweshshrimali5

Answer 23

yes but they have fixed values like G, h, c, etc.

Answer 24

Right.. I hope i can identify them..

G = Universal gravitational constant
h = planck's constant
c = speed of light

Sorry for off topic comment but : great work @Compassionate "sir"

Answer 25

.......you have too much time....
good effort.

Answer 26

Actually, c, can slow down in certain situations.

Answer 27

hmn right similarly as "g"

Answer 28

Not actually

Answer 29

c is speed of light IN VACUUM which is fixed

Answer 30

@Compassionate @mathslover c never changes it value except in quantum physics

Answer 31

OH k sorry

Answer 32

np

Answer 33

In some situations light can travel sideways, this decelerating it. I don't want to get into this. Bye. :)

Answer 34

Bye and best of luck

Answer 35

Bye and best of luck

Answer 36

Bye and best of luck

Answer 37

Copy and paste? "bye and best of luck" ?