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Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
BELLWORK – DAY #1
Solve.
1. n + 9 = 17
n=8
2. 6x = 42
x=7
3. 71 – z = 55
z = 16
y
4. 8 = 9
y = 72
2-6 Solving Two-Step Equations
BELLWORK – DAY #2
1. 0 = w + 4
2. n – 9 = -14
3. -3b = 36
4. -100 = -4u
5. d/5 = -7
6. c/4 = -20
2-6 Solving Two-Step Equations
BELLWORK – DAY #3
4. Brandon follows a 2,800 calorie-perday diet. He has 11 servings of breads and
cereals, which average 140 calories each.
Yesterday, he had a combined 9 servings of
fruits and vegetables, averaging 60 calories
each. How many 180-calorie servings of
meat and milk did he have to complete his
diet?
2-6 Solving Two-Step Equations
BELLWORK – DAY #4
1.
Last week, Carlie had several rice cakes and 3
granola bars as snacks. The snacks contained a total of
800 calories. If each granola bar had 120 calories and
each rice cake had 40 calories, how many rice cakes did
she have?
2.
Erika is following a 2,200 calorie-per-day diet. She
eats the recommended 9 servings of breads and cereals,
averaging 120 calories per serving. She also eats 5
servings of vegetables. If the rest of her daily intake is 870
calories, what is the average number of calories in each
serving of vegetables?
2-6 Solving Two-Step Equations
Sunshine State Standards Learning
Goal
MA.7.A.3.3 We will solve two-step
linear equations. MA.7.A.3.4
When you solve equations
that have one
operation, you use an
inverse operation to
isolate the variable.
n + 7 = 15
–7
–7
n
= 8
You can also use inverse
operations to solve equations that have more
than one operation.
2x + 3 = 23
–3 –3
2x
= 20
Use the inverse of
mulitplication to
isolate x.
Additional Example 1A: Solving Two-Step Equations
Using Division
Solve. Check each answer.
9c + 3 = 39
9c + 3 = 39
– 3 –3
9c
= 36
9c = 36
9
9
c=4
Subtract 3 from both sides.
Divide both sides by 9.
Additional Example 1A Continued
Check.
9c + 3 = 39
? 39
9(4) + 3 =
Substitute 4 for c.
? 39
36 + 3 =
? 39
39 =
4 is a solution.
Helpful Hint
Reverse the order of operations when
solving equations that have more
than one operation.
Additional Example 1B: Solving Two-Step Equations
Using Division
Solve. Check the answer.
–34 = –4m – 6
–34 = –4m – 6
+6
+6
–28 = –4m
–28 = –4m
–4
–4
7=m
Add 6 to both sides.
Divide both sides by –4.
Additional Example 1B Continued
Check.
–4m – 6 = –34
? –34
–4(7) – 6 =
Substitute 7 for m.
? –34
–28 – 6 =
?
–34 =
–34
7 is a solution.
2-6 Solving Two-Step Equations
rubric on solving two step equations
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
Check It Out: Example 1A
Solve.
3x + 13 = 37
3x + 13 = 37
– 13 –13
3x
= 24
3x = 24
3
3
x=8
Check It Out: Example 1B
Solve.
–33 = –7a – 5
–33 = –7a – 5
+5
+5
–28 = –7a
–28 = 7a
–7
–7
4
= a
2-6 Solving Two-Step Equations
rubric on solving two step equations
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
Additional Example 2A: Solving Two-Step Equations
Using Multiplication
Solve.
y
6 + 5 = 21
y
6+ 5
–6
y
5
(5) y
5
= 21
–6
= 15
Subtract 6 from both sides.
= (5)15
Multiply both sides by 5.
y = 75
Additional Example 2B: Solving Two-Step Equations
Using Multiplication
Solve.
5=z
6–7
5= z
6–7
+7
+7
12 = z
6
(6)12 = z (6)
6
72 = z
Add 7 to both sides.
Multiply both sides by 6.
Check It Out: Example 2A
Solve.
r
+ 45 = –60
7
r + 45 = –60
7
– 45
–45
r
=–105
7
r = (7)(–105)
(7)
7
r = –735
2-6 Solving Two-Step Equations
rubric on solving two step equations
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
Check It Out: Example 2B
Solve.
p
– 7 = 12
–8
p
– 7 = 12
–8
+7
+7
p
= 19
–8
(–8)
p
–8 = (–8)19
p = –152
Additional Example 3: Consumer Math Application
Jamie rented a canoe while she was on vacation.
She paid a flat rental fee of $85.00, plus $7.00
each day. Her total cost was $127.00. For how
many days did she rent the canoe?
Let d represent the number of days she rented the canoe.
7d + 85 = 127
– 85 –85 Subtract 85 from both sides.
7d
= 42
Divide both sides by 7.
7d = 42
7
7
d =6
Jamie rented the canoe for 6 days.
Check It Out: Example 3
Leo and his five brothers have $40 to spend on
movie tickets and popcorn. They pay $25 for the
tickets. If popcorn costs $3 per box, can each
person have his own box of popcorn? Explain.
Let b represent the number of boxes they can afford
to buy.
25 + 3b =
– 25
–
3b =
3b =
3
b=
40
25
15
15
3
5
Check It Out: Example 3 continued
No. For each person to have his own box, Leo
and his brothers must buy 6 boxes (one for Leo
and one for each brother). But they have enough
for only 5 boxes.
2-6 Solving Two-Step Equations
rubric on solving two step equations
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
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
Lesson Quiz
Solve. Check your answers.
1. 6x + 8 = 44
x=6
2. 14y – 14 = 28 y = 3
3. 12 = m + 3 63 = m
7
v
4. –8 – 6 = 8
v = –112
5. Last Sunday, the Humane Society had a 3-hour
adoption clinic. During the week the clinic is open
for 2 hours on days when volunteers are available.
If the Humane Society was open for a total of 9
hours last week, how many weekdays was the
clinic open? 3 days
Lesson Quiz for Student Response Systems
1. Solve 7q + 5 = 68.
A. q = 6
B. q = 7
C. q = 8
D. q = 9
Lesson Quiz for Student Response Systems
2. Solve 17h – 10 = 75.
A. h = 5
B. h = 7
C. h = 9
D. h = 10
Lesson Quiz for Student Response Systems
3. Solve
A. z = 72
B. z = 86
C. z = 90
D. z = 104
Lesson Quiz for Student Response Systems
4. A taxi charges an airport pickup fee of $3 plus
$1.50 for each mile traveled. If a taxi ride cost
John $36, how many miles did John travel in the
taxi?
A. 21 miles
B. 22 miles
C. 31 miles
D. 32 miles