Lesson Objective: I can… Lesson Topic: Finding Solutions to Make Equations True & From Equations to Inequalities Lesson Objective: I can… Define solution in the context of placing a value into a variable to see if that value makes the equation true. Understand that an inequality with numerical expressions is either true or false. Understand solving an inequality is answering the question which values from a specified set, if any, make the inequality true. 1:47 It’s important in the real world: Remind students of behavior goal

Vocabulary A number or value for the variable that results in a true number sentence is called a “solution to the equation” Example: Because the values that make n=9 true or false are the same as the values that make 8n=72 true or false, we can represent the solution as “The solution is 9” or n=9. 1:47 It’s important in the real world: finding and comparing locations with more than 2 directions Remind students of behavior goal

YOU have the power to change the number you insert into a variable A couple quick points… The domain of the variable is just the set of numbers from which we are looking for solutions. Sometimes we only want to consider integers as solutions. In those cases, the domain of the variable would be the set of integer numbers. YOU have the power to change the number you insert into a variable

Example 1 Directions: Which of the number(s) in the following set, if any, make the equation or inequality true: (0, 3, 5, 8, 10, 14)? 1:50

Yes, the number 6 will make the equation in part (c) true. Discussion How does the answer to part (a) compare to the answer to part (b)? Is there a number that we could include in the set so that part © will have a solution? In part (a), 8 is the only number that will result in a true number sentence. But in part (b), any number in the set that is less than 8 will make the number sentence true. Yes, the number 6 will make the equation in part (c) true. 1:50

Discussion Would 6 be part of the solution set in part (d)? How could we change part (d) so that 6 would be part of the solution? No, the 6 would not make part (d) a true number sentence because 6-4 is not greater than 2. If the greater than symbol was changed to the greater than or equal to symbol, we could include 6 in the solution set. 1:50

Any number greater than or equal to 16. Discussion Which whole numbers, if any, make the inequality true in part (f) true? Is it possible for every number in a set to result in a true number sentence? Any number greater than or equal to 16. Yes. For example, if the inequality says x>5 and all the numbers in the set are greater than 5, then all the numbers in the set will result in a true number sentence. 1:50

Discussion Consider the equation y + 3 = 11 and the inequality y + 3 < 11. How does the solution to the equation help you determine the solution set to the inequality? In the equation, y = 8 will result in a true number sentence. In the inequality, we want y + 3 to be a value less than 11. So, the numbers that will make it true must be less than 8. 1:50

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Lesson Summary Variable: a symbol (letter) that represents a number; a placeholder for a number Expression: An expression is a numerical expression or a result of replacing some (or all) of the numbers in a numerical expression with variables. Equation: a statement of equality between two expressions

Evaluate Your Learning 4 3 2 1 How will you “Sharpen Your Saw”? 2:17