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Holt CA Course 1 1-7 Equations and Their Solutions equation solution Vocabulary A mathematical statement that two quantities are equal. A value for a variable.

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Presentation on theme: "Holt CA Course 1 1-7 Equations and Their Solutions equation solution Vocabulary A mathematical statement that two quantities are equal. A value for a variable."— Presentation transcript:

1 Holt CA Course 1 1-7 Equations and Their Solutions equation solution Vocabulary A mathematical statement that two quantities are equal. A value for a variable that makes an equation true.

2 Holt CA Course 1 1-7 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

3 Holt CA Course 1 1-7 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. 12 + 15 27 s + 15 = 27 s = 12s = 10 10 + 15 27 s = 12 is a solution because 12 + 15 = 27. s = 10 is not a solution because 10 + 15  27.

4 Holt CA Course 1 1-7 Equations and Their Solutions Determine whether the given value of the variable is a solution. Example 1A: Determining Solutions of Equations b – 447 = 1,203 for b = 1,650 Because 1,203 = 1,203, 1,650 is a solution to b – 447 = 1,203. b – 447 = 1,203 Substitute 1,650 for b. 1,203 = 1,203 ? 1,650 – 447 = 1,203 ? 1,203 Subtract.

5 Holt CA Course 1 1-7 Equations and Their Solutions Determine whether the given value of the variable is a solution. Example 1B: Determining Solutions of Equations 27x = 1,485 for x = 54 Because 1,458  1,485, 54 is not a solution to 27x = 1,485. 27x = 1,485 Substitute 54 for x. 1,458 = 1,485 ? 27  54 = 1,485 ? 1,458 1,485 Multiply.

6 Holt CA Course 1 1-7 Equations and Their Solutions Determine whether the given value of the variable is a solution. 45  g = 3 for g = 15 Because 3 = 3, 15 is a solution to 45  g = 3. 45  g = 3 Substitute 15 for g. 3 = 3 ? 45  15 = 3 ? Check It Out! Example 1B 3 3 Divide.

7 Holt CA Course 1 1-7 Equations and Their Solutions You can use equations to check whether measurements given in different units are equal. For example, there are 12 inches in one foot. If you have a measurement in feet, multiply by 12 to find the measurement in inches: 12  feet = inches, or 12f = i. If you have one measurement in feet and another in inches, check whether the two numbers make the equation 12f = i true.

8 Holt CA Course 1 1-7 Equations and Their Solutions Paulo says that the park is 19 yards long. Jamie says that the park is 664 inches long. Determine if these two measurements are equal. Example 2: Measurement Application Because 684  664, 19 yards are not equal to 664 inches. Substitute 664 for i. 684 = 664 ? Multiply. 36  y = i 36  19 = 664 ? One yard has 36 inches. 36  y = 664 ? Substitute 19 for y.

9 Holt CA Course 1 1-7 Equations and Their Solutions Determine whether the given value of the variable is a solution. u + 56 = 139 for u = 73 Because 129  139, 73 is not a solution to u + 56 = 139. u + 56 = 139 Substitute 73 for u. 129 = 139 ? 73 + 56 = 139 ? Check It Out! Example 1 129 139 Add.

10 Holt CA Course 1 1-7 Equations and Their Solutions 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. Because 84 = 84, yes 7 feet is equal to 84 inches. Substitute. 84 = 84 ? 12  7 = 84 ? Check It Out! Example 2 12  ft = in. Multiply.


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