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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 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 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 Holt CA Course 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 = 12s = s = 12 is a solution because = 27. s = 10 is not a solution because  27.

4 Holt CA Course 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 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, x = 1,485 Substitute 54 for x. 1,458 = 1,485 ? 27  54 = 1,485 ? 1,458 1,485 Multiply.

6 Holt CA Course 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 =  g = 3 Substitute 15 for g. 3 = 3 ? 45  15 = 3 ? Check It Out! Example 1B 3 3 Divide.

7 Holt CA Course 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 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 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 ? = 139 ? Check It Out! Example Add.

10 Holt CA Course 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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