Algebra Made Easy(er)

By Mrs. Sinclair

Algebra? Balance? Say WHAT?

Question: “The triple of a number is 6. Can you guess whatthat number is?”

2Because you know that 3 times 2 equals 6.

Using the “language” of mathematics, the QUESTION can bestated as:

3x=6

By the way, 3Xis the same as 3 times x

“The triple of a number is 6.”

The sentence: "Can you guess what that numberis?” in math 'language' is

X = ?

“X” is the unknown number we need to find out.

Using the “language” of mathematics, the ANSWER can be stated as:

X = 2 “The number is 2”

Let’s start from the very beginning.

Looking at the equation, we don’t know the value of ‘x’ but we know oneimportant thing:

The LEFT side is EQUAL to the RIGHT side, and we have to believe thisand move on with our lives.

3x – 4 = 7 + 2xthis side is equal to this side

Now we arrive at the first confusion about equations: Both sides are equal“in value” only, not the way they look in the paper.

This is similar to stating:

2 + 3 = 5This side is equal to this side

Very easy to believe because you know that

2 plus 3 = 5, even if

2 + 3 is written differently than the number 5.

The ‘=’ sign is saying both sides are equal in value not in appearance.

So, when you get an equation to solve, you start by believing that the equalsign is telling the absolute truth: both sides are equal in value.

Our main goal :

The 'x' by its own

Let’s say we were given this statement

x + 7How can we get rid of the 7 so we keep only the x?

The x is being added 7 units so we make just the opposite: we subtract 7 units.

x + 7 - 7Because 7 – 7 is equal to zero both sevens disappear.

The x alone.

X - 2

X – 2 + 2

Let’s say we were given this statement

How can we get rid of the -2 so we keep only the x?

The x is being subtracted 2 units so we make just the opposite: we add 2 units.

Because -2 + 2 is equal to zero both 'twos' disappear.

The x is alone.

3xBreaking it down …

Let’s say we were given this statement

How can we get rid of the 3 so we keep only the x?

Well, if the number 3 is multiplying by x … we simply divide by 3 to get

3x3 Because 3 divided by 3 is equal to 1

we get x alone. x

Let’s say we were given this statementx5

How can we get rid of the 5 so we keep only the x?

The x is being divided by 5. In this case we multiply also by 5.

5x5

As 5 divided by 5 is equal to 1 both fives disappear.

The result is that we keep the x alone, as we wanted.

x

What does ‘equation’ mean?

3x – 4 = 7 + 2x

An equation looks like this:

And your main goal is to solve the equation so you get thevalue of the x (not known at this time) that makes theformula correct.

3x – 4 = 7 + 2xSolving means to know the value for 'x'.

We know the value of 'x' when we can say: 'x' is equal to …the left side of the equal sign.

X = ?Most important rule: Because both sides of an equation are EQUAL,any operation we do on one side must be done on the other side.

Most important rule: Because both sides of an equation are EQUAL,any operation we do on one side must be done on the other side.

3x – 4 = 7 + 2x

First step: Decide which side the variable will be on and write it above the equation. x = #

This will help you remember which side you are moving the # to and which side you are moving the variable to.

Most important rule: Because both sides of an equation are EQUAL,any operation we do on one side must be done on the other side.

3x – 4 = 7 + 2x-2x - 2x

x = #

Re-write what is left after you get your variable or # to one side.

x – 4 = 7

Most important rule: Because both sides of an equation are EQUAL,any operation we do on one side must be done on the other side.

x – 4 = 7 x = #

Now that my Variable is on the correct side, I need to get all my numbers to one side so the X stands alone. Continue with opposite math. Look at your diagram to get the #s where you wanted them.

+4 +4

Re-write what is left. x = 11

(x = #)

3x – 4 = 7 + 2x

3 * (11) – 4 = 7 + 2 * (11)

Check your workReplace the variable with your solution – then solve.33 – 4 = 7 + 22 29 = 29

Ta-Dah!You just correctly did Algebra!!!

Powerpoint Assembled by:

Mrs. Sinclair

Step-by-step instructions from:http://elementaryalgebra.pages3d.net/

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