LESSON 6: Solved algebra examples 2      
Introduction to Elementary Algebra
Help on solving algebra math problems
Simple step by step method
If you remember from Lesson 1: Things you should know before starting  we usually
use the last letters of the alphabet (x, y, z) for unknown numbers in Algebra equations.

In this example we will use the letter 'y' as the unknown number or 'variable' so you
get used to different letters. The rules are always the same.

So let us solve the following equation:
Question: What is the number that ‘y’ stands for?


We want something like
Where we have the ‘y’ is on the left side of the equation (by the way, it is called the
first member) and a number on the
right side of the equation (the second member).

Let’s start by taking all the 'y's to the first member. You can see that we must make
the 8y disappear because it is on the right side of equation and it should be on the
left side.
On the right side
Once again if you compare this step with the one before, it is as if we just moved the
-15y to the other member and changed the sign to plus ( +15y )

With enough practice this is the
fastest way to solve equations: you just move
numbers from one side to the other and change the sign.

However, what we are in fact doing is adding or subtracting from both sides of the
equation as it should be.



Now that we have all the 'y's on the first member it is time to make the numbers
disappear on the left side of the equation.

Let us begin with the number 2. To make it go, all we need to do is add -2 to BOTH
sides of the equation. Like this:
Which results as below
Congratulations!

The equation is solved !
Bye for now. More answers to algebra problems examples in a few days.
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Mathematical Algebra
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Introduction to Elementary Algebra. Help on solving algebra math problems. Simple step by step method
Introduction to Elementary Algebra. Easy Elementary algebra lessons are meant to teach equations in the simplest way.
Introdução à Algebra - Matemática Ajuda na resolução de problemas matemáticos de Algebra Simples método com explicações passo a passo
Introdução à Algebra - Matemática. Estas lições de algebra elementar têm como objectivo o ensino simplificado e eficiente da resolução de equações.
To do this we must subtract -8y from the right side of the equation because 8y - 8y
is equal to zero.

But if we do this to the second member (the right side) we must also do it on the
first member so the equation remains equal. Let us do it on both members:
We now have
equals zero and so disappears
If you compare the initial equation with this one just above you can see that the result
is the same as just moving the 8y from the right side to the left side of the equation but
changing the signal, from plus to minus.

Our next move is to make the -15y disappear on the second member. As you know by
now, what we have to do is to add 15y to the second member  and also on the first
member of the equation. Looks like this:
On the right side
We now have
equals zero and so disappears
On the left side
We now have
equals to zero and so disappears
Look that the number 2 magically changed sides and sign.


Finally we turn to the number 6.

Same thing here:
We now have
We very easy calculations we get
As you can notice the 'y' is almost alone on the first member of the equation, except for
that annoying number 4 next to it. Because the number 4 is
multiplying the 'y' we just
divide by 4 BOTH members of our equation:
        And our equation is solved.

To make sure that the 'y' is indeed the number -3, we substitute the 'y'
with -3 in the
initial (top of the page) given equation. Like this:
This result is an identity and the solution y = -3  is, therefore, correct.
17 = 17
Lesson 1: Things you should know before starting

Lesson 2: What does ‘equation’ mean?

Lesson 3: Our main goal: The 'x' by its own

Lesson 4: Ready to solve the equation

Lesson 5: Solved algebra examples 1

Lesson 6: Solved algebra exercises 2
2 - 3y + 6 - 8y
= - 4 - 15y
+ 15y
+ 15y