Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
3.2 Solving Equations: Review of the Addition and Multiplication Properties Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Equation vs. Expression Statements like 5 + 2 = 7 are called equations. An equation is of the form expression = expression. An equation can be labeled as Equal sign x + 5 = 9 left side right side Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6ed 2 Addition Property of Equality Let a, b, and c represent numbers. If a = b, then a+c=b+c and a–c=b-c In other words, the same number may be added to or subtracted from both sides of an equation without changing the solution of the equation. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6ed 3 Multiplication Property of Equality Let a, b, and c represent numbers and let c 0. If a = b, then a b a ∙ c = b ∙ c and c = c In other words, both sides of an equation may be multiplied or divided by the same nonzero number without changing the solution of the equation. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6ed 4 Solve for x. x-4=3 To solve the equation for x, we need to rewrite the equation in the form x = number. To do so, we add 4 to both sides of the equation. x-4=3 x - 4 + 4 = 3 + 4 Add 4 to both sides. x=7 Simplify. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6ed 5 Check To check, replace x with 7 in the original equation. x - 4 = 3 Original equation ? 7 - 4 = 3 Replace x with 7. 3 = 3 True. Since 3 = 3 is a true statement, 7 is the solution of the equation. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6ed 6 Solve for x 4x = 8 To solve the equation for x, notice that 4 is multiplied by x. To get x alone, we divide both sides of the equation by 4 and then simplify. 4x 8 = 4 4 1∙x = 2 or x = 2 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6ed 7 Check To check, replace x with 2 in the original equation. 4x = 8 Original equation 4 ∙ 2 = 8 Let x = 2. ? 8 = 8 True. The solution is 2. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6ed 8 Using Both Properties to Solve Equations 2(2x – 3) = 10 Use the distributive property to simplify the left side. 4x – 6 = 10 Add 6 to both sides of the equation 4x – 6 + 6 = 10 + 6 4x = 16 Divide both sides by 4. x=4 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6ed 9 Check To check, replace x with 4 in the original equation. 2(2x – 3) = 10 2(2 · 4 – 3) = 10 ? 2(8 – 3) = 10 ? (2)5 = 10 Original equation Let x = 4. True. The solution is 4. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra, 6ed 10