1. 2-3: Solving Multi-Step Equations
Essential Skills: Solve equations involving more than one operation
Solve equations involving consecutive integers

2. 2-3: Multi-Step Equations
Example 1A: Solve 2q + 11 = 3.
Solve using PEMDAS, backwards
2q + 11 = 3 Original equation
2q + 11 – 11 = 3 – 11 Subtract 11 from each side
2q = -8
2q/2 = -8/2 Divide each side by 2
q = -4

3. 2-3: Multi-Step Equations
Example 1B: Solve
Original equation
Multiply each side by 12
k + 9 = -24
k + 9 – 9 = -24 – 9 Subtract 9 from each side
k = -33

4. 1) Solve 6v + 7 = -5 v = -2 v = -6 v = 2 v = 1/3 1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19

5. 2) Solve
j = 17
j = -17
j = 19
j = -19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

6. 2-3: Multi-Step Equations
Example 2: Write an equation and solve the problem
Fourteen less than three fourths of a number is negative eight. Find the number.
¾n – 14 = -8 Translate to English
¾n – = Add 14 to each side
¾n = 6
4/3 ● ¾n = 4/3 ● 6 Multiply each side by 4/3
n = 8

7. 3) Three-fourths of the difference of a number
3) Three-fourths of the difference of a number and 7 is negative fifteen. What is the number?
-13
-15 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

8. 2-3: Multi-Step Equations
Consecutive Integers
Integers that come in counting order
Symbols: n, n + 1, n + 2, …
Example: …, -2, -1, 0, 1, 2, …
Consecutive Even Integers
Even integers followed by the next even integer
Symbols: n, n + 2, n + 4, …
Example: …, -2, 0, 2, 4 …
Consecutive Odd Integers
Odd integers followed by the next odd integer
Example: …, -1, 1, 3, 5, …

9. 2-3: Multi-Step Equations
Example 3: Write an equation for the problem below. Then solve the equation and answer the problem.
Find three consecutive odd integers whose sum is 57.
Let n = the first odd integer
Let n + 2 = the second odd integer
Let n + 4 = the third odd integer
The sum of three consecutive odd integers is 57
n + (n + 2) + (n + 4) = 57
3n + 6 = 57 Combine like terms
3n + 6 – 6 = 57 – 6 Subtract 6 from each side
3n = 51
3n/3 = 51/3 Divide each side by 3
n = 17

10. 2-3: Multi-Step Equations
Example 3 (continued)
The sum of three consecutive odd integers is 57
n + (n + 2) + (n + 4) = 57
3n + 6 = 57 Combine like terms
3n + 6 – 6 = 57 – 6 Subtract 6 from each side
3n = 51
3n/3 = 51/3 Divide each side by 3
n = 17
17 is the first integer
= 19 is the second integer
= 21 is the third integer

11. 4) Find three consecutive even integers whose sum is 84.
28, 30, 32
26, 28, 30
20, 20, 24
40, 20, 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

12. 2-3: Multi-Step Equations
Assignment
Page 93-94
1 – 29 (odds)
Must show work for credit