Equations and Their Solutions

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Equations and Their Solutions
Warm Up
Problem of the Day
Lesson Presentation
Course 1
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Warm Up Evaluate each expression for x 8. 1.
3x 5 2. x 8 3. 2x 7 4. 8x ? 4 5. 7x 1 6.
x 3
29
16
9
16
55
5
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Solving Subtraction Equations
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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Learn to determine whether a number is a solution
of an equation.
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Vocabulary
equation solution
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An equation is a mathematical statement that two
quantities are equal. You can think of a correct
equation as a balanced scale.
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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
s 12 is a solution because 12 15 27.
s 10 is not a solution because 10 15 ? 27.
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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
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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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
Substitute 54 for x.
Multiply.
Because 1,458 ? 1,485, 54 is not a solution
to 27x 1,485.
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Try This Example 1A
Determine whether the given value of the variable
is a solution.
u 56 139 for u 73
u 56 139
Substitute 73 for u.
Add.
Because 129 ? 139, 73 is not a solution to u
56 139.
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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
Substitute 15 for g.
Divide.
Because 3 3, 15 is a solution to 45 ? g 3.
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Additional Example 2
Paulo says that his yard is 19 yards long. Jamie
says that Paulos yard is 664 inches long.
Determine if these two measurements are equal.
36 ? yd in.
36 ? y 664
Substitute 19 for y
Multiply.
Because 684 ? 664, 19 yards are not equal to 664
inches.
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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
Substitute 7 for f.
Multiply.
Because 84 84, 7 feet is equal to 84 inches.
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Lesson Quiz
Determine whether the given value of the variable
is a solution. 1. 85 13x for x 5 2. w 38
210 for w 172 3. 8y 88 for y 11 4. 16 w ?
6 for w 98
no
yes
yes
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