2. 2.4 Variables & Equations Classify Equations and Determine Solutions

3. 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).

4. Types of Equations Equations are true, false, or open. True: 6 + 12 = 18 18 = 18 Of course it’s true. False: 6 = 4 + 3 6≠ 7 Both sides are not =, the equation is not balanced Open: 6y = -3 + 5y 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: 6 + 12 = 18 18 = 18 Of course it’s true. False: 6 = 4 + 3 6≠ 7 Both sides are not =, the equation is not balanced Open: 6y = -3 + 5y We have no idea if it’s true because we don’t know the value of y.... yet..

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

6. 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

7. Determining Solutions p. 81 170 + x = 200 Is 30 a solution? Write, sub, solve 170 + 30 = 200 200 = 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. 170 + x = 200 Is 30 a solution? Write, sub, solve 170 + 30 = 200 200 = 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.

8. Determining Solutions p. 81 8 + t = 2t Is 1 a solution? Write, sub, solve 8 + 1 = 2(1) 9 ≠ 2 No, 1 is not a solution Is 6 a solution to the equation 9 - m = 3 ? 9 - 6 = 3 3 = 3 Yes, 6 is a solution to this equation. 8 + t = 2t Is 1 a solution? Write, sub, solve 8 + 1 = 2(1) 9 ≠ 2 No, 1 is not a solution Is 6 a solution to the equation 9 - m = 3 ? 9 - 6 = 3 3 = 3 Yes, 6 is a solution to this equation.

9. 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 35+ 200 = 165 ? No, 235 ≠ 165

10. 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 6 + 27 = 33 ? Yes, 33 = 33

11. 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 -2 + 5 = 3 3 = 3 Yes, it is a solution. 24 = 2(c) + 29 24 = 2(-2) + 29 24 = -4 + 29 24 ≠ 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.

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