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Solving Linear Equations Objective: Identify and solve equations that are linear in nature. Title: Jul 31 ­ 2:11 PM (1 of 10) Linear equations are equations such as 3x + 12 = 0, 0.62x ­ 0.3 = 0 Sometimes a linear equation is called a first­degree equation, because the variable is of degree 1. Title: Jul 31 ­ 2:11 PM (2 of 10) Solve the equation: 3(x ­ 2) = 5(x ­ 1) 3x ­ 6 = 5x ­ 5 3x = 5x + 1 ­2x = 1 x = Title: Jul 31 ­ 2:11 PM (3 of 10) ­1 2 Notation The book uses brackets to show a finite set of solutions. This is called set notation. If Title: Jul 31 ­ 2:11 PM (4 of 10) the book will say, "The solution set is " Solve The solution set is Title: Jul 31 ­ 2:11 PM (5 of 10) Solve 9x ­ (7x ­ 1) = 2 9x ­7x + 1 = 2 2x + 1 = 2 2x = 1 1 2 { } Title: Jul 31 ­ 2:11 PM (6 of 10) Solve 2x = 2 + 1 x 5 3 2x 5 1 x 3 = 2 6 x 15 5 x = 2 15 1 x = 2 15 1 . x = 2 . 15 15 15 {30} Title: Jul 31 ­ 2:11 PM (7 of 10) Solve 2x = 2 + 1 x using another method. 5 3 Find the least common denominator (LCD) for the fractions in the problem, then multiply every term by the LCD. Title: Jul 31 ­ 2:11 PM (8 of 10) The LCD in this example is 15. 15 . 15 . 13 x 15 . 52 x = 2 + 6x = 30 + 5x x = 30 {30} Title: Jul 31 ­ 2:11 PM (9 of 10) Homework: pg. 998 #'s: 13­30 Title: Jul 31 ­ 2:11 PM (10 of 10)