Introduction to Elementary AlgebraHelp on solving algebra math problemsSimple 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:

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

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.

first member) and a number on the

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:

-15y to the other member and changed the sign to plus ( +15y )

With enough practice this is the

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.

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:

is equal to zero.

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:

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:

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:

that annoying number 4 next to it. Because the number 4 is

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:

To make sure that the 'y' is indeed the number -3, we substitute the 'y'

with -3 in the

This result is an identity and the solution y = -3 is, therefore, **correct**.

17 = 17

2 - 3y + 6 - 8y

= - 4 - 15y

+ 15y |

+ 15y |