1. Linear Equations
Doctor Shildneck

2. Vocabulary
Mathematical Expression – a mathematical statement that uses addition, subtraction, multiplication and division.
Equation – a relation that uses an equal sign to show the equivalence between two mathematical expression.
Linear Equation – an equation that is made up of linear expressions. (Remember, linear indicates first degree).

3. Solving Linear Equations
Goal: Determine the value of the unknown (variable) in an equation. This value makes the mathematical sentence TRUE.
To accomplish this task, we use inverse/opposite operations to undo all changes made to the variable.
That is, we want to get all of the numbers away from the variable in the expression so that we are left with an equation that states the value of the variable.

4. Procedure Get rid of any parentheses by DISTRIBUTION.
SIMPLIFY the expressions on each side of the equal sign.
Add or subtract to GET ALL INSTANCES OF THE VARIABLE ON ONE SIDE of the equal sign.
Add or subtract to GET ALL CONSTANTS ON THE OTHER SIDE of the equal sign.
Multiply or divide to GET RID OF THE COEFFICIENT of the variable.
REMEMBER: All Steps are completed to BOTH SIDES of an equation to keep it balanced.

5. Examples (1) PROCEDURE Parentheses Simplify Variable (one side, +/-)
Constant (other, +/-)
Coefficient (x/÷)

6. Examples (2) PROCEDURE Parentheses Simplify Variable (one side, +/-)
Constant (other, +/-)
Coefficient (x/÷)

7. Examples (3) PROCEDURE Parentheses Simplify Variable (one side, +/-)
Constant (other, +/-)
Coefficient (x/÷)

8. Examples (4) PROCEDURE Parentheses Simplify Variable (one side, +/-)
Constant (other, +/-)
Coefficient (x/÷)

9. Examples (5) PROCEDURE Parentheses Simplify Variable (one side, +/-)
Constant (other, +/-)
Coefficient (x/÷)

10. Examples (6) PROCEDURE Parentheses Simplify Variable (one side, +/-)
Constant (other, +/-)
Coefficient (x/÷)

11. Examples (7) PROCEDURE Parentheses Simplify Variable (one side, +/-)
Constant (other, +/-)
Coefficient (x/÷)

12. Examples (8) PROCEDURE Parentheses Simplify Variable (one side, +/-)
Constant (other, +/-)
Coefficient (x/÷)