the variable is alone on one side of the equal sign

the variable has a coefficient of 1

*

Variable

refers to a letter or symbol representing a quantity.

Your goal when solving an algebraic equation is to isolate the variable.

**Solving Algebraic Equations**

12 + 3x - 6 + 4x = 20

In Algebra a term is either:

* a single number, or

* a variable, or

* numbers and variables multiplied together.

6

+

7x

= 20

-6 -6

7x

= 14

12 + 3(

2

)- 6 + 4(

2

)= 20

(12 - 6) + (3(

2

) + 4(

2

))= 20

6 + 6 + 8 = 20

12 + 8 = 20

20 = 20

Example 2:

5(

4

) - 8 + 3 = 31 - 4(

4

)

An

equation

is a statement that two expressions separated by an equal sign have the same value.

Equation

1. Write the original equation.

2. Simplify the equation by combining like terms that are on the same side of the equal sign.

3. Undo any addition or subtraction using inverse operations.

4. Undo any multiplication or division using inverse operations.

5. Check the answer.

12

+

3x

- 6

+

4x

= 20

Below the like terms have been grouped together.

(12 - 6)

+

(3x + 4x)

= 20

The following is the simplified equation.

6

+

7x

= 20

Review the steps:

Prove you are right.

Once the equation has been simplified, use

inverse operations

to solve the equation.

Check the answer by substituting the solution into the original equation to see if it makes a true statement.

Replace each x with 2.

Algebraic Equation Example 1

First Combine Like Terms

12

+

3x

- 6

+

4x

= 20

________ __

_

Next, undo the operation taking place between the variable and its coefficient. Since x is being multiplied by 7, the inverse operation is to divide both sides of the equal sign by the coefficient of x in order to make the coefficient of x to equal 1.

In this example, 12 and -6 are like terms and 3x and 4x are like terms.

7x

= 14

7 7

x = 2

Use

inverse operations

to solve the equation.

______ _____

Only

like terms

may be combined through addition or subtraction.

Adding

unlike terms

is like adding apples and oranges,

it does not make sense.

12 + 3x +(-6) + 4x = 20

If the same variable is on both sides of the equal sign,

remove the variable with the smallest value from each side of the equal sign using inverse operations.

Now that the variable, x is only on one side of the equal sign,undo the addition of

-5

.

Undo the operation taking place between the variable and its coefficient. The variable, x is being multiplied by its

coefficient, 9

.

So divide both sides of the e

qual sign

by

9

.

12 +(-6)+ 3x + 4x = 20

Combine

Like Terms

to simplify.

6

and

7x

are not like terms. Therefore, we may not add them together. The only way to get

7x

alone is to remove

6

.

To remove a

positive 6

the

inverse operation

is to add a negative 6 to both sides of the equal sign.

6+(-6)+7x = 20 +(-6)

Add -6 to both sides of the equal sign in order to create zero pairs and isolate the variable.

7x = 14

We now know that 7x equals 14.

But we want to know what one x equals.

x = 2

5x

- 8 + 3

= 31 - 4x

5x

- 5

= 31 - 4x

5x

- 5

= 31 - 4x

+4x

+ 4x

9x

- 5

= 31

9x

- 5

= 31

+ 5 + 5

9x

= 36

**9x**

= 36

= 36

6

+

7x

= 20

-6 -6

_______ __

7x

= 14

___ ___

7 7

x = 2

5x + (-

8)

+ 3

= 31 - 4x

5x +

(-5)

= 31 - 4x

+4x + 4x

________ ___

9x - 5 = 31

+ 5 + 5

_

_ __

9 9

x = 4

_______ ___

9

x = 36

9

5x - 8 + 3 = 31 - 4x

Combine like term that are on the same side of the equal sign.

Example 2:

**9**

x

= 36

x

= 36

In other words, use inverse operations

.

**x = 4**

**9 9**

5x - 8 + 3 = 31 - 4x

20 - 5 = 31 - 16

15 = 15

To find the value of one x, we divide 14 evenly between each x to determine how much one x is worth.

12

+

3x

- 6

+

4x

= 20

(12 - 6)

+

(3x + 4x)

= 20

6

+

7x

= 20

Why both sides?

We add

-6 to both sides because

like a balance, what you

do to one side you must do to the other side to

remain balanced.

12 + 3x -6 + 4x = 20

12

+

(-6)

+

3x

+

4x

= 20

7

**9**