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2-5 Solving Equations Containing Integers
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
2-5 Solving Equations Containing Integers
BELLWORK – DAY #1
Use mental math to find each solution.
1. 7 + y = 15
y=8
2. x ÷ 9 = 9
x = 81
3. 6x = 24
x=4
4. x – 12 = 30
x = 42
2-5 Solving Equations Containing Integers
BELLWORK – DAY #2
Zelda sold her wet suit to a friend for
$156. She sold her tank, mask, and
snorkel for $85 less than she sold her
wet suit. She bought a used wet suit for
$80 and a used tank, mask, and snorkel
for $36. If she started with $0, how
much money does she have left?
$111
2-5 Solving Equations Containing Integers
BELLWORK – DAY #3
Use mental math to find each solution.
1. 9 + e = 34
e = 25
2. r ÷ 12 = 5
r = 60
3. 12h = 132
h = 11
4. j – 14 = 50
j = 64
5. 65 – k = 31
k = 34
2-5 Solving Equations Containing Integers
Sunshine State Standards Learning
Goal
MA.7.A.3.3 We will formulate and use
different strategies to solve one-step linear
equations. MA.7.A.3.4
2-5 Solving Equations Containing Integers
Additional Example 1A: Solving Addition and
Subtraction Equations
Solve each question. Check each answer.
–6 + x = –7
–6 + x = –7
+6
+6
x = –1
Check
Add 6 to both sides to
isolate the variable.
–6 + x = –7
?
–6 + (–1) = –7
?
–7 = –7 
Substitute –1 for x.
True.
2-5 Solving Equations Containing Integers
Additional Example 1B: Solving Addition and
Subtraction Equations
Solve each equation. Check each answer.
p + 5 = –3
p + 5 = –3
+ (–5) +(–5)
Add –5 to both sides.
p = –8
Check
p + 5 = –3
?
–8 + 5 = –3
?
– 3 = –3 
Substitute –8 for p.
True.
2-5 Solving Equations Containing Integers
Additional Example 1C: Solving Addition and
Subtraction Equations
Solve each equation. Check each answer.
y – 9 = –40
y – 9 = –40
+9
+9
Check
Add 9 to both sides.
y = –31
y – 9 = –40
?
–31 – 9 = –40
?
–40 = –40 
Substitute –31 for y.
True.
2-5 Solving Equations Containing Integers
1
2
3
4
5
No
understanding
Little
understanding
Some
understanding
Good
understanding
Complete
understanding
No
comprender
Poca
comprension
Una Cierta
comprension
Buena
comprension
Comprension
Completa
Pa gen okenn
konpreyansyon
Ti
konpreyansyon
Kek
konpreyansyon
Bon konprann
Ranpli
konpreyansyon
2-5 Solving Equations Containing Integers
Check It Out: Example 1
Solve each equation. Check your answer.
A. y – 7 = –34
y – 7 = –34
+7
+7
y
= –27
B. – 7 + b =
9
–7 + b = 9
+7
+7
b = 16
2-5 Solving Equations Containing Integers
Check It Out: Example 1
Solve each equation. Check each answer.
C. m – 5 = –12
m – 5 = –12
+5
+5
m
= –7
2-5 Solving Equations Containing Integers
Additional Example 2A: Solving Multiplication and
Division Equations
Solve each equation. Check each answer.
b =6
–5
b =6
–5
b
(–5) –5
= (–5)6
b = –30
Multiply both sides by –5.
2-5 Solving Equations Containing Integers
1
2
3
4
5
No
understanding
Little
understanding
Some
understanding
Good
understanding
Complete
understanding
No
comprender
Poca
comprension
Una Cierta
comprension
Buena
comprension
Comprension
Completa
Pa gen okenn
konpreyansyon
Ti
konpreyansyon
Kek
konpreyansyon
Bon konprann
Ranpli
konpreyansyon
2-5 Solving Equations Containing Integers
Additional Example 2A Continued
Check
b =6
–5
?
–30 =
6
–5
6 = 6
Substitute –30 for b.
True.
b = 6.
–5
2-5 Solving Equations Containing Integers
Additional Example 2B: Solving Multiplication and
Division Equations
Solve each equation. Check each answer.
–400 = 8y
–400 = 8y
–400 = 8y
8
8
–50 = y
Divide both sides by 8.
2-5 Solving Equations Containing Integers
Additional Example 2B: Solving Multiplication and
Division Equations
Check
–400 = 8y
Substitute –50 for y.
?
–400 = 8(–50)
–400 = –400 
True.
2-5 Solving Equations Containing Integers
1
2
3
4
5
No
understanding
Little
understanding
Some
understanding
Good
understanding
Complete
understanding
No
comprender
Poca
comprension
Una Cierta
comprension
Buena
comprension
Comprension
Completa
Pa gen okenn
konpreyansyon
Ti
konpreyansyon
Kek
konpreyansyon
Bon konprann
Ranpli
konpreyansyon
2-5 Solving Equations Containing Integers
Check It Out: Example 2A
Solve each equation. Check your answer.
c = –12
4
c = –12
4
4
c
= (4)(–12)
4
c
= –48
2-5 Solving Equations Containing Integers
Check It Out: Example 2B
Solve each equation. Check your answer.
6a = –366
6a = –366
366
6a
=–
6
6
a = –61
2-5 Solving Equations Containing Integers
Check It Out: Example 2C
Solve each equation. Check your answer.
–12d = 144
–12d = 144
–12d = 144
–12
–12
d = –12
2-5 Solving Equations Containing Integers
Check It Out: Example 2D
Solve each equation. Check your answer.
h = –7
9
h = –7
9
9
h
= (9)(–7)
9
h
= –63
2-5 Solving Equations Containing Integers
1
2
3
4
5
No
understanding
Little
understanding
Some
understanding
Good
understanding
Complete
understanding
No
comprender
Poca
comprension
Una Cierta
comprension
Buena
comprension
Comprension
Completa
Pa gen okenn
konpreyansyon
Ti
konpreyansyon
Kek
konpreyansyon
Bon konprann
Ranpli
konpreyansyon
2-5 Solving Equations Containing Integers
Additional Example 3: Business Application
In 2007, a manufacturer made a profit of $300
million. This amount was $100 million more than
the profit in 2006. What was the profit in 2006?
Let p represent the profit in 2006 (in millions of dollars).
2007 profit
300
is
=
100 million More than
+
100
300 = 100 + p
–100 –100
200 = p
The profit was $200 million in 2006.
2006 profit
p
2-5 Solving Equations Containing Integers
Check It Out: Example 3A
In July, a department store made a profit of
$50 thousand. This amount was $17 thousand
less than the profit in June. What was the
profit in June?
Let p represent the profit in June (in thousands of
dollars).
Profit in July = p – 17
Profit in July = $50 thousand
2-5 Solving Equations Containing Integers
Check It Out: Example 3A continued
p – 17 =
50
+ 17
+ 17
p
=
67
The profit in June was $67 thousand.
2-5 Solving Equations Containing Integers
Check It Out: Example 3B
In 2008, a manufacturer made a profit of $450 million. A negative profit is considered a
loss. This amount was $125 million more than
the profit in 2007. What was the profit in
2007?
Let p represent the profit in 2007 (in millions of
dollars).
Profit in 2008 = p + 125
Profit in 2008 = $–450
2-5 Solving Equations Containing Integers
Check It Out: Example 3B Continued
p + 125 =
–450
–125
– 125
p
= –575
The profit in 2007 was –$575 million.
2-5 Solving Equations Containing Integers
1
2
3
4
5
No
understanding
Little
understanding
Some
understanding
Good
understanding
Complete
understanding
No
comprender
Poca
comprension
Una Cierta
comprension
Buena
comprension
Comprension
Completa
Pa gen okenn
konpreyansyon
Ti
konpreyansyon
Kek
konpreyansyon
Bon konprann
Ranpli
konpreyansyon
2-5 Solving Equations Containing Integers
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
2-5 Solving Equations Containing Integers
CHAP. 2-5 (BLUE) LESSON QUIZ
Solve each equation. Check your answer.
1. –8y = –800
2. x – 22 = –18
3. – y = 7
7
100
4
–49
4. w + 72 = –21 –93
5. Last year a phone company had a loss of $25
million. This year the loss is $14 million more
last year. What is this years loss? $39 million
2-5 Solving Equations Containing Integers
Lesson Quiz for Student Response Systems
5. In an online test, Rick scored –34 points.
This was 20 points less than his previous
score. What was his previous score?
A. 54 points
B. 14 points
C. –14 points
D. –54 points