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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