Lesson 2.1 Expressions, Equations, and Inequalities Objective- To recognize symbols, variables, and types of sentences used in algebra. Equalities Inequalities < Is less than = Equals- is the same as > Is greater than Congruent- same size and shape Is less than or equal to ~ Approx. equal to Similar- same shape = Not equal to Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

A variable represents an unknown value. What is a variable? A variable represents an unknown value. 1) 3 + ___ = 10 2) 6 + = 9 These are all variables 3) 8 + x = 12 4) 5 + = 8 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Expressions vs. Equations Sentences Expressions Equations Inequalities 2 + 3 2 + 3 = 5 9 - 5 > 3 Numerical 5(8) - 4 4 + 2(3) = 10 x + 7 x - 4 = 13 Variable 6y - 4 < 8 8 - 3y 11= 3 + 2m Open sentences Open sentences have solutions and can be solved. Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Identify each as an expression, sentence, open sentence, equation, or inequality. 1) 3x + 5 = 11 Sentence, open sentence, equation 2) 7 < 2(5) + 3 Sentence, inequality 3) 5x - 2 Expression 4) 6m + 2 > 3 Sentence, open sentence, inequality Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Variable Inequalities Open sentences have solutions and can be solved. Variable Equations Variable Inequalities 4 + m = 7 5 + y < 91 - 4 - 4 - 5 - 5 m = 3 y < 86 Infinite Solutions One Solution Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Replacement Sets x(x - 2) = 0 -2(-2 - 2) = 8 -1(-1 - 1) = 2 Replacement set- an exclusive set of numerical values that may be used to solve an equation. Solve the equation over the set { -2, -1, 0, 1, 2 }. x(x - 2) = 0 Lock Ring of Keys Strategies 1) Look at the keys. 2) Try each key. Must find all that work! -2(-2 - 2) = 8 No -1(-1 - 1) = 2 No 0(0 - 2) = 0 Yes 1(1 - 2) = -1 No 2(2 - 2) = 0 Yes Solution: { 0, 2 } Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Solve each sentence below using the replacement set { 0, 1, 2, 3, 4, 5 }. { 5 } 1) x + 4 = 9 { 3 } 2) 5 - x = 2 { } or No Solution 3) 2x + 3 = 17 4) { 0, 1 } Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Give three solutions to each sentence below. 1) x > 10 Samples: 11, 15, 34 2) x + 3 7 Samples: 4, -8, 0 3) 5 - x < 0 Samples: 6, 7, 10 4) Samples: 2, -1, -2 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series