Simplifying Expressions and

Solving Equations

Mr. K’s Seven Steps for Solving

Equations

1. DistributeExample: Use the distributive property.

5( 1) 2( 4) 6

5 5 2 8 6

x x

x x

2. Combine Like Terms on Same side of the equals sign

8 65 5 2

5 5 42 1

x x

x x

3. Collect all variables on one side of the equals sign by + or -.

5 5 2 14

5 5 2 14

2

5 4

2

3 1

x

x

x

x

x

x

x

4. Collect all constants on one side of the equals sign by + or -.

5

5 14

3

3

9

5

x

x

5. Divide out the coefficient of the variable to isolate the variable.

3

3 9

3 9

93

3

x

x

x

6. Simplify fractions if needed.

3

9

3

x

x

7. Check your answer Mr. K’s way!

5 1 2 4 6

5 1 2 4 6

5 4 ?2 7 6

20 ? 14 6

20 20

3

3

x x

What is an Additive Inverse?

• When using addition, and two values are combined, their sum is …..

• ZERO

What is the Additive Inverse?

1. 8

2. 6

3.

4. - 5

5.

1

2

2

3

1

2

8

5

2

3

6

Vocabulary• Equation– A mathematical statement that

two expressions are equal (has an equal sign)

• Solution of an Equation– Value of the variable that

makes the statement true

Finding Solutions

• In order to find solutions we must, Isolate the Variable

• A variable is ISOLATED if it appears by itself on one side of the equation and not at all on the other side of the equation

Solving Expressions• In order to solve any mathematical

expression we must always follow the order of operations

•PEMDAS• P – Please Parentheses• E – Excuse Exponents• M – My Multiply• D – Dear Divide• A – Aunt Add• S – Sally Subtract

Solving Variable Equations

• In order to Isolate the variable, we sometimes need to move terms in the equations

• REMEMBER– When combining terms on the same side

of the EQUAL SIGN, you keep the SAME sign of the terms and just add them together

– We only use the OPPOSITE sign when we have to cross the equal sign

– This is because we are removing it from one side of the equal sign and adding it to the other side of the equal sign

4 5 2 1 3x y x y

Moving Terms

• First look at the problem and decide which operations you have and do you have to move them across an equal sign

• If you do we must do the Inverse Operation in reverse order of the Order of Operations

Inverse Operations

Operation Inverse Operation

Addition Subtraction

Subtraction Addition

Multiplication Division

Division Multiplication

Examples

10 4x

8 2b

7 9x

Signs When Multiplying and Dividing

• Rules–Multiply

– Divide

Examples

45

k

1.53

m

Examples

7 56x

535

9v

Homework

• Worksheet