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Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.1 – Slide 5 Linear Equation in One Variable A linear equation in one variable can be written in the form Ax + B = C where A, B, and C are real numbers, with A ≠ 0. 2.1 The Addition Property of Equality Identifying Linear Equations Some examples of linear and nonlinear equations follow. 4x + 9 = 0, 2x – 3 = 5, and x = 7 Linear x 2 + 2x = 5, = 6, and |2x + 6| = 0 Nonlinear

Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.1 – Slide 6 2.1 The Addition Property of Equality Identifying Linear Equations A solution of an equation is a number that makes the equation true when it replaces the variable. Equations that have exactly the same solution sets are equivalent equations. A linear equation is solved by using a series of steps to produce a simpler equivalent equation of the form x = a number or a number = x.

Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.1 – Slide 7 Addition Property of Equality If A, B, and C are real numbers, then the equations A = B and A + C = B + C are equivalent equations. In words, we can add the same number to each side of an equation without changing the solution. 2.1 The Addition Property of Equality Using the Addition Property of Equality

Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.1 – Slide 8 Note Equations can be thought of in terms of a balance. Thus, adding the same quantity to each side does not affect the balance. 2.1 The Addition Property of Equality Using the Addition Property of Equality

Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.1 – Slide 9 Example 1 Solve each equation. Our goal is to get an equivalent equation of the form x = a number. (a) x – 23 = 8 x – 23 + 23 = 8 + 23 2.1 The Addition Property of Equality Using the Addition Property of Equality x = 31 Check: 31 – 23 = 8 (b) y – 2.7 = –4.1 y – 2.7 + 2.7 = –4.1 + 2.7 y = – 1.4 Check: –1.4 – 2.7 = –4.1

Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.1 – Slide 10 2.1 The Addition Property of Equality Using the Addition Property of Equality The same number may be subtracted from each side of an equation without changing the solution. If a is a number and –x = a, then x = – a.

Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.1 – Slide 11 (a) –12 = z + 5 –12 – 5 = z + 5 – 5 2.1 The Addition Property of Equality Using the Addition Property of Equality –17 = z Check: –12 = –17 + 5 (b) 4a + 8 = 3a 4a – 4a + 8 = 3a – 4a 8 = –a Check: 4(–8) + 8 = 3(–8) ? –8 = a –24 = –24 Example 2 Solve each equation. Our goal is to get an equivalent equation of the form x = a number.

Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.1 – Slide 12 Example 3 Solve. 5(2b – 3) – (11b + 1) = 20 10b – 15 – 11b – 1 = 20 2.1 The Addition Property of Equality Simplifying and Using the Addition Property of Equality –b – 16 = 20 Check: 5((2 · –36) –3) – (11(–36) + 1) = –b – 16 + 16 = 20 + 16 –b = 36 b = –36 5(–72 –3) – (–396 + 1) = 5(–75) – (–395) = –375 + 395 = 20