Section 2.3 Solving Multi Step Equations

1. MULTI-STEP
EQUATIONS
Section 2.3 pages 91-96

2. Previously
11𝑥 = 77
11𝑥
11
=
77
11
Divide by 11 on both sides
𝑥 = 7

3. Multi-Step Equations
■ More than one operation to solve
■ Work backwards in order of operations
■ Undo all operations to isolate the variable

4. Solve the equation
2𝑎 − 6 = 4
+6 + 6
2𝑎 = 10
÷ 2 ÷ 2
𝑎 = 5

5. Solve the equation
𝑛 + 1
−2
= 15−2 ∙ ∙ −2
𝑛 + 1 = −30
−1 − 1
𝑛 = −31

6. Translate and then solve
Twelve decreased by twice a number is -34.
12 − 2𝑥 = −34
−12 − 12
−2𝑥 = −46
÷ −2 ÷ −2
𝑥 = 23

7. A Multi Part Problem
If 3𝑚 + 4 = −11, what is the value of 2𝑚 + 14?
Part 1: Find the value of 𝑚 by solving the given equation.
Part 2: Substitute in what you found to evaluate the value of the given expression.
3𝑚 + 4 = −11
3𝑚 = −15
𝑚 = −5
2𝑚 + 14
2(−5) + 14
−10 + 14
4
The answer to the question is 4.

8. Algebra 1i Homework
Page 94-95 #11-22, 24, 25, 48-50

9. Consecutive Integers
■ Integers that come in counting order
■ For example 4, 5, 6 can be written as 𝑛, 𝑛 + 1, 𝑛 + 2
■ n is the first of the consecutive integers

10. Consecutive Odd or Even Integers
■ Odd or Even numbers in counting order
■ Skips every other number
■ Must add 2 each term
■ Consecutive Odd example: 5, 7, 9 can be written as 𝑛, 𝑛 + 2, 𝑛 + 4
■ Consecutive Even example: 12, 14, 16 can be written as 𝑛, 𝑛 + 2, 𝑛 + 4

11. Write an equation and solve
Find three consecutive integers with a sum of 21.
Add 𝑛, 𝑛 + 1, 𝑎𝑛𝑑 , 𝑛 + 2 to equal 21
𝑛 + 𝑛 + 1 + 𝑛 + 2 = 21
3𝑛 + 3 = 21
3𝑛 = 18
𝑛 = 6
𝑛 + 1 = 7
𝑛 = 6
𝑛 + 2 = 8
The three integers are 6, 7, and 8.

12. Algebra 1 Homework
Page 94-95 #24-39, 42-50