2.4 Variables & Equations Classify Equations and Determine Solutions

Definitions Equation: An equation is a mathematical statement that says one quantity is equal to another quantity. Solution: A solution is a value that makes an equation true (balanced). Equation: An equation is a mathematical statement that says one quantity is equal to another quantity. Solution: A solution is a value that makes an equation true (balanced).

Types of Equations Equations are true, false, or open. True: = = 18 Of course it’s true. False: 6 = ≠ 7 Both sides are not =, the equation is not balanced Open: 6y = y We have no idea if it’s true because we don’t know the value of y.... yet.. Equations are true, false, or open. True: = = 18 Of course it’s true. False: 6 = ≠ 7 Both sides are not =, the equation is not balanced Open: 6y = y We have no idea if it’s true because we don’t know the value of y.... yet..

Test and Classify Each Equation 9 – 7 = 38 + x = 24(5) = 20 2 ≠ 3 ?20 = 20 FalseOpenTrue

Writing Equations: Locate Operational Words Nine times the opposite of 5 is forty-five 9(-5) = 45 Times (of course) is to multiply. The opposite of 5 is (-5). Our state of being verb indicates the = sign. -45 = 45 This equation is false. Write and classify an equation for “twenty minus x is three.” 20 – x = 3 Open

Determining Solutions p x = 200 Is 30 a solution? Write, sub, solve = = 200 Yes, 30 is a solution Is 17 a solution to the equation 9 = y – 10? 9 = 17 – 10 9 ≠ 7 No, 17 is not a solution to this equation x = 200 Is 30 a solution? Write, sub, solve = = 200 Yes, 30 is a solution Is 17 a solution to the equation 9 = y – 10? 9 = 17 – 10 9 ≠ 7 No, 17 is not a solution to this equation.

Determining Solutions p t = 2t Is 1 a solution? Write, sub, solve = 2(1) 9 ≠ 2 No, 1 is not a solution Is 6 a solution to the equation 9 - m = 3 ? = 3 3 = 3 Yes, 6 is a solution to this equation. 8 + t = 2t Is 1 a solution? Write, sub, solve = 2(1) 9 ≠ 2 No, 1 is not a solution Is 6 a solution to the equation 9 - m = 3 ? = 3 3 = 3 Yes, 6 is a solution to this equation.

Check Understanding p. 82 Diving equipment weighs 35 lb. If the diver and the equipment together weigh 165, could the diver weigh 200 lb? + = = 165 ? No, 235 ≠ 165

Check Understanding p. 82 A tent weighs 6lb. Your backpack and tent together weigh 33lb. Use an equation to find if the backpack weighs 27 lb. += = 33 ? Yes, 33 = 33

Apply the Skill…Work the Process For each equation, determine if -2 is a solution. c = -2 For each equation, determine if -2 is a solution. c = -2 c + 5 = = 3 3 = 3 Yes, it is a solution. 24 = 2(c) = 2(-2) = ≠ 25 No, it’s not a solution. 8 = 2(c + 6) 8 = 2([-2] + 6) 8 = 2(4) 8 = 8 Yes, it is a solution.

Finis Tomorrow we will begin to solve equations. Be patient and work the process. The simple steps will quickly become more complex.