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Equation Solutions & Applications: Mathematical Statements and Solutions

hoshiko-miyamoto avatar
hoshiko-miyamoto
9 diapositives · 212 Views · Nov 13, 2014

Learn how to determine solutions of equations and check if two quantities are equal using mathematical statements. Discover practical measurement applications. Examples provided.

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Equation Solutions & Applications: Mathematical Statements and Solutions
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  1. Vocabulary equation solution A mathematical statement that two quantities are equal. A value for a variable that makes an equation true.

  2. 3 + 2 5 An equation is a mathematical statement that two quantities are equal. You can think of a correct equation as a balanced scale.

  3. 10 + 15 27 12 + 15 27 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.

  4. ? 1,650– 447 = 1,203 ? 1,203 1,203 1,203 = 1,203 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.

  5. ? 2754 = 1,485 1,458 ? 1,485 1,458 = 1,485 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.

  6. 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.

  7. ? ? 36  y = 664 36  19 = 664 ? 684 = 664 Example 2: Measurement Application 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. One yard has 36 inches. 36  y = i Substitute 664 for i. Substitute 19 for y. Multiply. Because 684  664, 19 yards are not equal to 664 inches.

  8. ? 73 + 56 = 139 129 ? 139 129 = 139 Check It Out! Example 1 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.

  9. ? ? 84 = 84 12  7= 84 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. Substitute. Multiply. Because 84 = 84, yes 7 feet is equal to 84 inches.