1. 1. 2. Warm-up The inverse operation of addition is subtraction
The inverse operation of division is multiplication

2. 2.2 Solving Equations

3. California
Standards
Preparation for 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

4. How would we solve 3x + 5 = 12?
Let’s take another look at the balance
3x + 5
– 5 12
– 5
Subtract 5 from both sides

5. How would we solve 3x + 5 = 12?
Let’s take another look at the balance 3x 7
Subtract 5 from both sides
Simplify

6. Divide both sides by coefficient of the variable (3)
How would we solve 3x + 5 = 12?
Let’s take another look at the balance 3x 7 3 3
Subtract 5 from both sides
Simplify
Divide both sides by coefficient of the variable (3)

7. Divide both sides by coefficient of the variable (3)
How would we solve 3x + 5 = 12?
Let’s take another look at the balance 7 x 3
Subtract 5 from both sides
Simplify
So the solution is:
Divide both sides by coefficient of the variable (3)

8. 2x + 5 =11
–5 –5
2x = 6
Subtract 5 from both sides of the equation.
Divide both sides of the equation by 2.
x = 3
The solution set is {3}.
Each time you perform an inverse operation, you create an equation that is equivalent to the original equation. Equivalent equations have the same solutions, or the same solution set. In the example above, 2x + 5 = 11, 2x = 6, and x = 3 are all equivalent equations.

9. Let’s try one together. 3x + 4 = 25 -4 -4 0 21 3x = 21 3 3 x = 7
Directions
Step 1. Undo addition/subtraction
Remember that whatever you do to one side, you have to do to the other!!!!******
Step 2. Undo multiplication/division.
Step 3. Solve for the variable.

10. Two step equations - 4 -4 -7 7 y = -7 (7) 1 7 y = -49
Let’s try again. First: add or subtract. Second : divide or multiply Third: Is the variable isolated?

11. Let’s try some more equations
Remember, we have to keep the equations balanced!
Solve:
8m – 10 = 36
8m – =
8m = 46
m =
w = 84

12. The Box Method Let’s try to solve backwards… 6x – 11 = 13 × 6 - 11 x ?
+ 11
÷ 6 13 4 24
X = 4

13. Equations with Faction: Multiply by the least common denominator (LCD) to clear fractions.
Multiply both sides by 8, the LCD of the fractions.
Distribute 8 on the left side.
Simplify. Since 6 is subtracted from y, add 6 to both sides to undo the subtraction.
y – 6 = 10
y = 16
The solution set is {16}.

14. Now you try… 1. 3x – 7 = 2 4. 2. 4x + 1 = -3 5. 3. 5t – 2 = –32 x = 3

15. Challenge
1.5 = 1.2y – 5.7 J f
6 = y

16. Application
Sara paid $15.95 to become a member at a gym. She then paid a monthly membership fee. Her total cost for 12 months was $ How much was the monthly fee? 1
Locate key words in the question. UNDERLINE WHAT YOU ARE BEING ASKED TO FIND
The answer will be the monthly fee that Sara had paid during the year.

17. Reread and circle relevant information2
Reread and circle relevant information
Sara paid $15.95 to become a member at a gym. She then paid a monthly membership fee. Her total cost for 12 months was $ How much was the monthly fee?
Reread the part of the problem you underlined, and define an appropriate variable (or variables) 3
Let m represent the monthly fee that Sara paid.

18. Write an equation (or inequality) and then check to see if it’s correct by rereading the circled and underlined information 4
Sara paid $15.95 to become a member at a gym. She then paid a monthly membership fee. Her total cost for 12 months was $ How much was the monthly fee?
Circled info:
M = monthly fee
Sara paid that fee for 12 months.
She must also add the cost of the membership
initial fee
Monthly fee
plus is
total cost.
12m =
735.95
15.95 +

19. m = $60 month Solve the equation 12m + 15.95 = 735.95 –15.95 –15.954
12m =
– –15.95
12m =
Since is added to 12m, subtract from both sides to undo the addition.
Since m is multiplied by 12, divide both sides by 12 to undo the multiplication.
m = $60 month

20. Check your answer 12m + 15.95 = 735.95 12(60) + 15.95 = 735.95= =

21. Lynda has 12 records in her collection
Lynda has 12 records in her collection. She adds the same number of new records to her collection each month. After 7 months Lynda has 26 records. How many records does Lynda add each month?
r = 2 records a month

22. Lesson Quiz
Solve each equation.
1. 4y + 8 = x = 11 4 –8
5. Nancy bought 5 rolls of color film and 6 rolls of black-and-white film. The 5 rolls of color film cost $15, and Nancy’s total was $39. Write and solve an equation to find the cost of one roll of black-and-white film.
6b + 15 = 39; $4