1. Exercise
In what order would you perform these operations?
2 + 3(4)

2. Exercise
In what order would you perform these operations?
4 ÷ 2 + 3

3. Exercise
In what order would you perform these operations?
2 − 8 3

4. Exercise What inverse operation would you perform to solve for x?

5. Exercise What inverse operation would you perform to solve for x? x 2
= 5
x 2

6. Exercise What inverse operation would you perform to solve for x?

7. Example
3x − 8 = 28

8. Addition Property of Equality
How do you undo:
addition?
subtraction?
multiplication?
division?

9. Order of Operations
Symbols of grouping–evaluate quantities within symbols of grouping first.
Exponents– evaluate a term with an exponent before performing other operations.

10. Order of Operations
Multiplication and division– perform these operations in order from left to right.
Addition and subtraction– perform these operations last, in order from left to right.

11. Example l l l Simplify −4 + 3(−6) − 5(−7 + 3 • 6).
−4 + (−18) − 5(−7 + 18) l
−22 − 5(11) l
22 − 5(11)
22 − 55
= −33

12. Solving Equations with Two Operations
Determine the order in which the operations have been performed on the variable.

13. Solving Equations with Two Operations
Undo the operations in reverse order by performing the inverse operations on both sides of the equation.

14. Example 1
Solve 2n + 7 = 25, and check the solution.

15. First n is multiplied by 2; then 7 is added to the product.
Subtract 7 from both sides; then divide both sides by 2.

16. Example 2
Solve 3x − 4 = −10, and check the solution.

17. First x is multiplied by 3; then 4 is subtracted from the product.
Add 4 to both sides; then divide both sides by 3.

18. Example 3
z − 3 2
Solve = 9, and check
the solution.

19. First 3 is subtracted from z; then the difference is divided by 2.
= 9
First 3 is subtracted from z; then the difference is divided by 2.
Multiply both sides by 2; then add 3 to both sides.

20. Example 4
x 4
Solve = 20, and check
the solution.

21. First x is divided by 4; then 6 is added to the quotient.
+ 6 = 20
x 4
First x is divided by 4; then 6 is added to the quotient.
Subtract 6 from both sides; then multiply both sides by 4.

22. Example 5
Solve 5 − x = 10, and check the solution.

23. Example 6
This year the team won three more than twice as many games as last year. This year they won 75 games. How many games did they win last year?
Let g = the games won last year.

24. Example 6
The 1st two sentences begin with the words “This year.” Both refer to the same quantity. Write an expression for the first sentence followed by an equal sign and the value from the 2nd sentence.
2g + 3 = 75

25. Example 6 Subtract 3 from both sides. 2g + 3 = 75 2g = 72
Divide both sides by two.
2g = 72
g = 36

26. Example 7
Tony bought a trumpet for $498. He made a down payment of $46 and arranged to make payments of $55 per month. How many months will it take him to pay for the trumpet?

27. Example 7 Let m = the number of months.
Write an expression for the total payment ($55 per month plus the down payment).
55m + 46

28. Example 7
The expression representing the total amount paid must equal the cost of the trumpet.
55m + 46 = 498
Subtract 46 from both sides.
55m = 452
Divide both sides by 55.
m = 8.2 or 9 months

29. Exercise
Solve.
= −3
4a + 5 9

30. Exercise
Solve.
= −18
−6x + 6 7

31. Exercise
Solve.
−9z − 36 − 6 = 48

32. Exercise
Solve.
−y 4
+ 3 = 8

33. Exercise
Solve.
2x 13
− 6 = 4