This document discusses equations and their solutions. It provides examples of determining if a given value is a solution to an equation by substituting the value for the variable and evaluating if it makes the equation true. It also gives examples like comparing measurements in feet and inches to see if they are equal. The document aims to teach how to determine if a number is a solution to an equation.

1. 2-4 Equations and Their Solutions
2-4 Equations and Their Solutions
Warm Up
Problem of the Day
Lesson Presentation
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2. 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
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3. 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
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4. 2-4 Equations and Their Solutions
Learn to determine whether a number is a
solution of an equation.
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5. 2-4 Equations and Their Solutions
Vocabulary
equation
solution
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6. 2-4 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 5
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7. 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 s = 10
10 + 15
12 + 15 27 27
s = 12 is a solution s = 10 is not a solution
because 12 + 15 = 27. because 10 + 15 ≠ 27.
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8. 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 Substitute 1,650 for b.
?
1,203 = 1,203 Subtract.
1,203 1,203
Because 1,203 = 1,203,
1,650 is a solution to
b — 447 = 1,203.
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9. 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 Substitute 54 for x.
?
1,458 = 1,485 Multiply.
1,458
1,485 Because 1,458 ≠ 1,485,
54 is not a solution to
27x = 1,485.
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10. 2-4 Equations and Their Solutions
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 Substitute 73 for u.
?
129 = 139 Add.
129
139 Because 129 ≠ 139,
73 is not a solution to
u + 56 = 139.
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11. 2-4 Equations and Their Solutions
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.
?
3=3 Divide.
3 3
Because 3 = 3,
15 is a solution to
45 ÷ g = 3.
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12. 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 Substitute.
?
684 = 664 Multiply.
Because 684 ≠ 664, 19 yards are not equal to 664
inches.
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13. 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 Substitute.
?
84 = 84 Multiply.
Because 84 = 84, 7 feet is equal to 84 inches.
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14. 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 if Kylee paid the correct amount of
money. (Hint: $8 • pizzas = total cost.) no
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