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2-4
Equations and Their Solutions
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
2-4
Equations and Their Solutions
Warm Up
Evaluate each expression for x = 8.
1. 3x + 5
29
2. x + 8
16
3. 2x – 7
9
4. 8x  4
16
5. 7x – 1
55
6. x – 3
5
2-4
Equations and Their Solutions
Problem of the Day
Complete the magic square so that every
row, column, and diagonal add up to the
same total.
9
2
10
8
7
6
4
12
5
2-4
Equations and Their Solutions
Learn to determine whether a number is a
solution of an equation.
2-4
Equations and Their Solutions
Vocabulary
equation
solution
2-4
Equations and Their Solutions
An equation is a mathematical statement
that two expressions are equal. You can think
of a correct equation as a balanced scale.
3+2
5
2-4
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.
10 + 15
27
s = 10 is not a solution
because 10 + 15  27.
2-4
Equations and Their Solutions
Reading Math
The symbol  means “is not equal to.”
2-4
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
1,203
Substitute 1,650 for b.
Subtract.
Because 1,203 = 1,203,
1,650 is a solution to
b — 447 = 1,203.
2-4
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
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
2-4
Check It Out: 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.
Equations and Their Solutions
2-4
Check It Out: 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.
2-4
Equations and Their Solutions
Reading Math
An equation has an equal sign, but an
expression does not. An equation can be
solved, but an expression can only be
evaluated or simplified.
2-4
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  19 = 664
?
684 = 664
Substitute.
Multiply.
Because 684  664, 19 yards is not equal to 664
inches.
2-4
Equations and Their Solutions
Check It Out: 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.
?
12  7 = 84
?
84 = 84
Substitute.
Multiply.
Because 84 = 84, 7 feet is equal to 84 inches.
2-4
Equations and Their Solutions
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
2-4
Equations and Their Solutions
Lesson Quiz
Determine whether the given value of each
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 whether Kylee paid the correct amount of
money. (Hint: $8 • pizzas = total cost.) no
2-4
Equations and Their Solutions
Lesson Quiz for Student Response Systems
1. Identify the value of the variable that is
the solution of the 9z = 63.
A. z = 17
B. z = 14
C. z = 54
D. z = 72
2-4
Equations and Their Solutions
Lesson Quiz for Student Response Systems
2. Identify the value of the variable that is the
solution of the equation x – 125 = 375.
A. x = 3
B. x = 250
C. x = 490
D. x = 500
2-4
Equations and Their Solutions
Lesson Quiz for Student Response Systems
3. Identify the value of the variable that is the
solution of the equation 48 = 6w.
A. w = 8
B. w = 42
C. w = 54
D. w = 288
2-4
Equations and Their Solutions
Lesson Quiz for Student Response Systems
4. Identify the value of the variable that is the
solution of the equation k  7 = 13.
A. k = 6
B. k = 20
C. k = 71
D. k = 91
2-4
Equations and Their Solutions
Lesson Quiz for Student Response Systems
5. The saleswoman at a bakehouse charged
Deborah $64 for 16 burgers. The price of
burger is $4. Determine whether Deborah
paid the correct amount of money.
A. yes; the cost of 16 burgers is $64
B. no; the cost of 16 burgers is $60
C. no; the cost of 16 burgers is $58
D. no; the cost of 16 burgers is $56