Download 2-3

6th Grade Math: Chapter 2 LEARNING GOAL
Students will understand variables, expressions,
and equations by being able to do the following:
• Identify and Evaluate Expressions (2-1)
• Translate between Words and Math (2-2)
• Determine Whether a Number is a Solution of an Equation (2-3)
• Solve Whole-Number Addition Equations (2-4)
• Solve Whole-Number Subtraction Equations (2-5)
• Solve Whole-Number Multiplication Equations (2-6)
• Solve Whole-Number Division Equations (2-7)
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Equations and Their Solutions
HW: Pg. 54 #8-23 ANSWERS
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Equations and Their Solutions
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Equations and Their Solutions
th
6
Grade Math HW
Page 60
#8-20 all
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Equations and Their Solutions
Warm Up
Problem of the Day
Lesson Presentation
Course
Course 11
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Equations and Their Solutions
Warm Up
Evaluate each expression for x = 8.
1.
2.
3.
4.
5.
6.
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3x + 5
x+8
2x – 7
8x  4
7x – 1
x–3
29
16
9
16
55
5
Equations
and Their Equations
Solutions
2-3 Solving
Subtraction
Problem of the Day
Complete the magic square so that every
row, column, and diagonal add up to the
same total.
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9
2
10
8
7
6
4
12
5
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Equations and Their Solutions
Today’s Learning Goal
Learn to determine
whether a number
is a solution of an
equation.
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Equations and Their Solutions
Vocabulary
equation
solution
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Equations and Their Solutions
An equation is a mathematical statement
that two quantities are equal. You can think of
a correct equation as a balanced scale.
3+2
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Equations and Their Solutions
Equations may contain variables. If a value for
a variable makes an equation true, that value
is a solution of the equation.
s + 15 = 27
s = 12
12 + 15
s = 10
27
s = 12 is a solution
because 12 + 15 = 27.
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10 + 15
27
s = 10 is not a solution
because 10 + 15  27.
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Equations and Their Solutions
Additional Example 1A: Determining Solutions of
Equations
Determine whether the given value of the
variable is a solution.
b — 447 = 1,203 for b = 1,650
b — 447 = 1,203
?
1,650 — 447 = 1,203
?
1,203 = 1,203
1,203
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1,203
Substitute 1,650 for b.
Subtract.
Because 1,203 = 1,203,
1,650 is a solution to
b — 447 = 1,203.
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Equations and Their Solutions
Additional Example 1B: Determining Solutions of
Equations
Determine whether the given value of the
variable is a solution.
27x = 1,485 for x = 54
27x = 1,485
?
27  54 = 1,485
?
1,458 = 1,485
1,458
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1,485
Substitute 54 for x.
Multiply.
Because 1,458  1,485,
54 is not a solution to
27x = 1,485.
Equations and Their Solutions
2-3
Try This: Example 1A
Determine whether the given value of the
variable is a solution.
u + 56 = 139 for u = 73
u + 56 = 139
?
73 + 56 = 139
?
129 = 139
129
139
Substitute 73 for u.
Add.
Because 129  139,
73 is not a solution to
u + 56 = 139.
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Equations and Their Solutions
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Try This: Example 1B
Determine whether the given value of the
variable is a solution.
45  g = 3 for g = 15
45  g = 3
?
45  15 = 3
Substitute 15 for g.
?
Divide.
3=3
3
3
Because 3 = 3,
15 is a solution to
45  g = 3.
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Equations and Their Solutions
Additional Example 2
Paulo says that his yard is 19 yards long.
Jamie says that Paulo’s yard is 664 inches
long. Determine if these two measurements
are equal.
36  yd = in.
36  y = 664
?
36  19 = 664
?
684 = 664
Substitute 19 for y
Multiply.
Because 684  664, 19 yards are not equal to
664 inches.
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Equations and Their Solutions
Try This: Example 2
Anna says that the table is 7 feet long. John
says that the table is 84 inches long.
Determine if these two measurements are
equal.
12  ft. = in.
12f = 84
?
12  7 = 84
?
84 = 84
Substitute 7 for f.
Multiply.
Because 84 = 84, 7 feet is equal to 84 inches.
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Equations and Their Solutions
Lesson Quiz
Determine whether the given value of the
variable is a solution.
1. 85 = 13x for x = 5 no
2. w + 38 = 210 for w = 172 yes
3. 8y = 88 for y = 11 yes
4. 16 = w  6 for w = 98 no
5. The local pizza shop charged Kylee $172 for 21
medium pizzas. The price of a medium pizza is $8.
Determine if Kylee paid the correct amount of
money. (Hint: $8 • pizzas = total cost.) no
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