1. Solving Equations with the Variable on Each Side
Lesson 3-5
Solving Equations with the Variable on Each Side 

4. Objectives Solve equations with the variable on each side
Solve equations involving grouping symbols

5. Vocabulary
Identity – an equation that is true for every value of the variable

6. Steps for Solving Equations
Step 1: Use the Distributive Property to remove the grouping symbols, () or []
Step 2: Simplify the expressions on each side of the equal sign “=” by combining like terms (variable and #’s)
Step 3: Use the Addition and /or Subtraction Properties of Equality to get the variables on one side of the equal sign and the numbers without variables on the other side of the equals sign
Step 4: Simplify the expressions on each side of the equals sign by combining like terms
Step 5: Use the Multiplication and/or Division Properties of Equalities to solve for the variable

7. Example 1 Solve . Original equation Subtract 7s from each side.
Simplify.
Subtract 8 from each side.
Simplify.
Divide each side by –2.
Answer: s = 5
Simplify.

8. Example 2 Solve . Then check your solution. Original equation
Distributive Property
Subtract 12q from each side.
Simplify.
Subtract 6 from each side.

9. Example 2 cont Simplify. Divide each side by –8. Answer: q = 6
To check, substitute 6 for q in the original equation.

10. Example 3 Solve . Original equation Distributive Property
Subtract 40c from each side.
This statement is false.
Answer: There must be at least one c to represent the variable. This equation has no solution.

11. Example 4 Solve . Then check your solution. Original equation
Distributive Property
Answer: Since the expression on each side of the equation is the same, this equation is an identity. The statement is true for all values of t.

12. Example 5 A. Multiple-Choice Test Item Solve Answer: D
A B – C D –26
Answer: D
B. Multiple-Choice Test Item
Solve
A B – C D –26
Answer: C

13. Summary & Homework Summary: Homework: Combine like terms
Separate variables and numbers to different sides of the equation, “=”
Solve for the variable
Homework:
pg 152-3; even