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2.1 Equations, Formulas, and the Problem-Solving Process 1. Verify solutions to equations. 2. Use formulas to solve problems. What’s the difference? x3 x3 5 Expression Simplified Equation Solved Equation: Two expressions set equal. 23 5 True 73 5 False Solution: A number that makes an equation true when it replaces the variable in the equation. x 2 is the solution. To Check a Possible Solution Replace the variable in the equation with the value. If the resulting equation is true, the value is a solution. Solutions Is a = 12 a solution? Use parentheses! 4a 7 51 4 7 51 412 7 51 48 7 51 55 51 NO Solutions 6 Is x a solution? 5 8x 3 2x 15 6 6 8 3 2 15 5 5 48 12 3 15 5 5 48 15 12 75 5 5 5 5 63 63 5 5 Yes Determine which of the following is a solution for the equation. 6 x 4 2 4 x 3 6 a) –5 b) – 1 c) 2 d) 4 2.1 Determine which of the following is a solution for the equation. 6 x 4 2 4 x 3 6 a) –5 b) – 1 c) 2 d) 4 2.1 Formula: An equation that describes a mathematical relationship. Perimeter: Area: The distance around a figure. The total number of square units that fill a figure. Volume: The total number of cubic units that fill a space. Circumference: Radius: The distance around a circle. The distance from the center of a circle to any point on the circle. Diameter: The distance across a circle through its center. Formulas See page 95!!!! Area: A lw w Perimeter: P 2l 2w l Area: h 1 A bh 2 b Area: r A r 2 Circumference: C 2r C d Formulas Perimeter, Area or Volume? Filling a pool with water? Volume Cover for a pool? Area Tile around a pool? Perimeter Fencing? Perimeter Laying carpet? Area Putting up a wallpaper border? Perimeter Formulas Suppose you have a rectangular pool that is 12 feet wide and 20 feet long. The pool has a constant depth of 4 feet. Find the perimeter, the area and the volume. Perimeter: P 2l 2w P 220 212 P 40 24 P 64 feet Formulas Suppose you have a rectangular pool that is 12 feet wide and 20 feet long. The pool has a constant depth of 4 feet. Find the perimeter, the area and the volume. Area: A lw A 20 12 A 240 square feet or ft2 Formulas Suppose you have a rectangular pool that is 12 feet wide and 20 feet long. The pool has a constant depth of 4 feet. Find the perimeter, the area and the volume. Volume: V lwh V 20 124 V 960 cubic feet or ft3 A thermometer reads 30° C: what is this temperature in degrees Fahrenheit? 9 F C 32 5 a) 34F b) 49F c) 86F d) 112F 2.1 A thermometer reads 30° C: what is this temperature in degrees Fahrenheit? 9 F C 32 5 a) 34F b) 49F c) 86F d) 112F 2.1