1. Objectives:
Solve equations that contain variable terms on both sides.

2. Inverse Operations
To solve equations we isolate (get by itself) variables by using inverse operations.
The following needs to be memorized:
Inverse Operations
Addition
Subtraction
Multiplication
Division
Square x2
Square Root

3. Steps to solving ALL equations
Clear parenthesis (Use distributive Property)
Combine Like Terms on each side of the =
Move all variables to one side of the “=“ using inverse operations (+ or -)
Move all constants (numbers) to the other side of the “=“ using inverse operations (+ or -)
Get rid of the constant (number) attached to the variable by either (x or ÷)

4. 1. Solve 7n – 2 = 5n + 6
2. Solve 4b + 2 = 3b

5. 4. Solve
4(2x – 5) = 5x + 4
3. Solve
7x + 2 = 5x + 8

6. 5. Solve Solve
y = 0.7y – 0.3
3x + 15 – 9 = 2(x + 2)

7. A video store has two movie rental plans
A video store has two movie rental plans. Plan A includes a $25 membership fee plus $1.25 for each movie rental. Plan B costs $40 for unlimited movie rentals.
For what number of movie rentals is plan B the same as plan A?

8. The Home Cleaning Company charges $312 to power-wash the siding of a house plus $12 for each window. Power Clean charges $36 per window, and the price includes power-washing the siding.
How many windows must a house have to make the total cost from each cleaning company the same?

9. An identity is an equation that is true for all values of the variable
An identity is an equation that is true for all values of the variable. An equation that is an identity has infinitely many solutions EXAMPLE: 5=5
A contradiction is an equation that is not true for any value of the variable. It has no solutions EXAMPLE 0=5

10. 9. Solve
10 – 5x + 1 = 7x + 11 – 12x
10. Solve
12x – 3 + x = 5x – 4 + 8x

11. 11. Solve
4y + 7 – y = y
12. Solve
2c c = –14 + 3c + 21

12. Day 2

13. Objectives:
Solve inequalities that contain variable terms on both sides.

14. REMEMBER:
The only difference between solving equations and inequalities is:
WHEN SOLVING INEQUALITIES… IF YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER YOU MUST FLIP THE SIGN!!!!!

15. 2. Solve
-2t – 6 < 5t + 1
Solve
4m – 3 < 2m + 7

16. 4. Solve
5(2 – r) ≥ 3r – 6
3. Solve
2(k – 3) > 6 + 3k – 3

17. 5. Rick bought a photo printer and supplies for $186
5. Rick bought a photo printer and supplies for $186.90, which will allow him to print photos for $0.29 each. A photo store charges $0.55 to print each photo.
How many photos must Rick print before his total cost is less than getting prints made at the photo store?

18. Identity – Solutions are ALL REAL NUMBERS.
There are special cases of inequalities called identities and contradictions.
Identity – Solutions are ALL REAL NUMBERS.
If you solve the inequality and you get a true statement
Example 6 < 10
Contradictions – NO SOLUTION
If you solve the inequality and you get a false statement
Example: 5 < 2

19. 6. Solve
2x – 7 ≤ 5 + 2x
7. Solve
2(3y – 2) – 4 ≥ 6y + 21