Solving Two-Step and
2-3 Multi-Step Equations
Warm Up
Simplify each expression.
1. 9 –3(–2)
2. 3(–5 + 7)
3.
4. 26 – 4(7 – 5)
Simplify each expression.
5. 10c + c
6. 8.2b + 3.8b – 12b
7. 5m + 2(2m – 7)
8. 6x – (2x + 5)
Solving Two-Step and
2-3 Multi-Step Equations
Learning Goals
1.  Students will solve and check multi-step equations
2. Students will solve and check multi-step equations involving fractions
3. Students will solve and check multi-step equations involving distributive
property and combining like terms
4. Students will identify important information from an application problem
and use that information to set up and solve an equation
Solving Two-Step and
2-3 Multi-Step Equations
Notice
Alex
belongs
that this
to equation
a music club.
contains
In this
multiplication
club, students
can buy
and
addition.
a student
Equations
discount
thatcard
contain
for $19.95.
more than
Thisone
card allows
operation
require
them to
more
buythan
CDs one
for $3.95
step toeach.
solve.
After
one year,the
Identify
Alex
operations
has spent
in$63.40.
the equation and the
order in which they are applied to the variable.
To find the number of CDs c that Alex bought, you
Then use inverse operations and work backward to
can solve an equation.
undo them one at a time.
Cost per CD
Total cost
Cost of discount card
Solving Two-Step and
2-3 Multi-Step Equations
Operations in the Equation
To Solve
1. First c is multiplied
by 3.95.
1. Subtract 19.95 from
both sides of the
equation.
2. Then 19.95 is added.
2. Then divide both sides
by 3.95.
Solving Two-Step and
2-3 Multi-Step Equations
Example 1A: Solving Two-Step Equations
Solve
A. 18 = 4a + 10
B. 5t – 2 = –32
C. –4 + 7x = 3
D.
1.5 = 1.2y – 5.7
E.
Solving Two-Step and
2-3 Multi-Step Equations
Example 1A: Solving Two-Step Equations
Solve
a. 24 = 3b + 9
b. 6y – 6 = –36 c. –10 + 7t = 4
d.
d
e. 6 + 5 = 2
3.2 = 1.2x – 7.6
€
Solving Two-Step and
2-3 Multi-Step Equations
Example 2A: Solving Two-Step Equations That
Contain Fractions
Solve
A.
D.
B.
C.
E.
Solving Two-Step and
2-3 Multi-Step Equations
Example 2a: Solving Two-Step Equations That
Contain Fractions
Solve
4
5 1
b.
r + =
5
4 5
a.
y − 5 = 1
7 6 21
€
c.
3x − 1 = 6
4
€
2
3 5
d.
u + =
3
4 6
e.
1 n − 1 = 3
3
€
5
8
2
Solving Two-Step and
2-3 Multi-Step Equations
Equations that are more complicated
may have to be simplified before they
can be solved. You may have to use the
Distributive Property or combine
like terms before you begin using
inverse operations.
Solving Two-Step and
2-3 Multi-Step Equations
Solve
Example 3A: Add Like Terms Before Solving
A.
8x – 21 + 5x = –15 B.
10y – (4y + 8) = –20
C.
2a + 3 – 8a = 8
D.
–2(3 – d) = 4
Solving Two-Step and
2-3 Multi-Step Equations
Solve
Example 3a: Add Like Terms Before Solving
a.
6x – 21 - 3x = –15
c.
4(x – 2) + 2x = 40
b.
5y – (2y + 4) = –10
d.
–4(2 –4d) = 24
Solving Two-Step and
2-3 Multi-Step Equations
Example 4: Application
Jan joined the dining club at the local café for
a fee of $29.95. Being a member entitles her
to save $2.50 every time she buys lunch. So
far, Jan calculates that she has saved a total
of $12.55 by joining the club. Write and solve
an equation to find how many time Jan has
eaten lunch at the café.
Solving Two-Step and
2-3 Multi-Step Equations
Jan joined the dining club at the local café for a fee
of $29.95. Being a member entitles her to save
$2.50 every time she buys lunch. So far, Jan
calculates that she has saved a total of $12.55 by
joining the club. Write and solve an equation to find
how many time Jan has eaten lunch at the café.
1
Understand the Problem
List the important information:
Solving Two-Step and
2-3 Multi-Step Equations
Jan joined the dining club at the local café for a fee
of $29.95. Being a member entitles her to save
$2.50 every time she buys lunch. So far, Jan
calculates that she has saved a total of $12.55 by
joining the club. Write and solve an equation to find
how many time Jan has eaten lunch at the café.
2
Make a Plan
Write an equation (a table may be helpful)
Solving Two-Step and
2-3 Multi-Step Equations
Jan joined the dining club at the local café for a fee
of $29.95. Being a member entitles her to save
$2.50 every time she buys lunch. So far, Jan
calculates that she has saved a total of $12.55 by
joining the club. Write and solve an equation to find
how many time Jan has eaten lunch at the café.
3
Solve
Solving Two-Step and
2-3 Multi-Step Equations
Jan joined the dining club at the local café for a fee
of $29.95. Being a member entitles her to save
$2.50 every time she buys lunch. So far, Jan
calculates that she has saved a total of $12.55 by
joining the club. Write and solve an equation to find
how many time Jan has eaten lunch at the café.
4 Look Back
What is an answer that is too high/low?
Solving Two-Step and
2-3 Multi-Step Equations
Sara paid $15.95 to become a member at a gym.
She then paid a monthly membership fee. Her total
cost for 12 months was $735.95. How much was
the monthly fee?
1
Understand the Problem
2
Make a Plan
3
Solve
4
Look Back
Solving Two-Step and
2-3 Multi-Step Equations
Lesson Quiz: Part 1
Solve each equation.
1. 4y + 8 = 2
2.
3. 2y + 29 – 8y = 5
4. 3(x – 9) = 30
5. x – (12 – x) = 38
6.
Solving Two-Step and
2-3 Multi-Step Equations
Lesson Quiz: Part 2
7. If 3b – (6 – b) = –22, find the value of 7b.
8. Josie bought 4 cases of sports drinks for an
upcoming meet. After talking to her coach,
she bought 3 more cases and spent an
additional $6.95 on other items. Her receipts
totaled $74.15. Write and solve an equation
to find how much each case of sports drinks
cost.