Unit 3 Day 4: Solving Multi-Step Equations
Notes
Name: ___________________________________ Date: _______________
Solve Multi-Step Equations:
 Equations that require more than one step to solve are called
__________________________________________.
 To solve these equations, we must undo each operation by working
_______________________.
Example 1: Solve Multi-Step Equations:
 Solve each equation. Check your solution.
a. 11𝑥 − 4 = 29
b.
𝑎+7
8
=5
Guided Practice:
 Solve each equation. Check your solution.
1A. 2𝑎 − 6 = 4
1B.
𝑛+1
−2
= 15
Period: _____
Real-World Example 2:
2
 SHOPPING Hiroshi is buying a pair of water skis that are on sale for 3 of the original
price. After he uses a $25 gift certificate, the total cost before taxes is $115. What was
the original price of the skis? Write an equation for the problem. Then solve the
equation.
Guided Practice 2A:
2
 RETAIL A music store has sold 5 of their hip-hop CDs, but 10 were returned. Now the
store has 62 hip-hop CDs. How many were there originally?
Guided Practice 2B:
3
 READING Len read of a graphic novel over the weekend. Monday, he read 22 more
4
pages. If he has read 220 pages, how many pages does the book have?
Solve Consecutive Integer Problems:
 _____________________________________ are integers in counting order, such as 4,
5, and 6 or 𝑛, 𝑛 + 1, and 𝑛 + 2.
 Counting by two will result in ________________________________________ if the
starting integer n is even and ________________________________________ if the
starting integer n is odd.
Concept Summary: Consecutive Integers
Type
Words
Symbols
Example
Consecutive
Integers
Integers that come in
counting order.
𝑛, 𝑛 + 1, 𝑛 + 2, …
… , −2, −1,0,1,2, …
Consecutive
Even Integers
Even integer followed
by the next even
integer.
𝑛, 𝑛 + 2, 𝑛 + 4, …
… , −2,0,2, 4, …
Consecutive Odd
Integers
Odd integer followed
by the next odd
integer.
𝑛, 𝑛 + 2, 𝑛 + 4, …
… , −1,1,3, 5, …
Example 3: Solve a Consecutive Integer Problem
 NUMBER THEORY Write an equation for the following problem. Then solve the
equation and answer the problem.
Find three consecutive odd integers with a sum of -51.
Guided Practice 3:
 Write an equation for the following problem. Then solve the equation and answer the
problem.
Find three consecutive integers with a sum of 21.
Check For Understanding - Example 1:
 Solve each equation. Check your solution.
3
1. 3𝑚 + 4 = −11
4.
2. 12 = −7𝑓 − 9
5. 8 =
𝑎
3. −3 = 2 + 11
6.
2
𝑎 − 8 = 11
𝑐+1
−3
𝑥−5
7
= −21
Check For Understanding – Example 2:
7. NUMBER THEORY Twelve decreased by twice a number equals -34. Write an equation
for this situation and then find the number.
8. BASEBALL Among the career home run leaders for Major League Baseball, Hank Aaron
has 175 fewer than twice the number that Dave Winfield has. Hank Aaron hit 755 home
runs. Write an equation for this situation. How many home runs did Dave Winfield hit
in his career?
Check For Understanding – Example 3:
 Write an equation and solve each problem.
9. Find three consecutive odd integers with a sum of 75.
10. Find three consecutive integers with a sum of -36.