1. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Section 2.1 The Addition Principle of Equality

2. 2 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Equations An equation uses an equal sign (=) and indicates that two expressions are equal. 6 + 7 = 13 An equation always has an equal sign. 6 + 7 = x The solution of an equation is the number which makes the equation true. 6 + 7 = 13 13 is the solution for this equation since it makes 6 + 7 = x true.

3. 3 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Equivalent Equations Equations that have exactly the same solution are called equivalent equations. x = 7 7 is the solution to the equation 6 + x = 13. 6 + x = 13 The process of finding all solutions of an equation is called solving the equation.

4. 4 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. The Addition Principle 6 + x = 13 Left sideRight side We need to find the value of x. 6 + x + (  6) = 13 + (  6) Adding (  6) to both sides of the equation will maintain the balance of the equation. x = 7 Solution to the equation. The Addition Principal If the same number is added to both sides of an equation, the results on both sides are equal in value.

5. 5 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example a  6.2 =  3.5 Check your answer in the original equation. a  6.2 + (6.2) =  3.5 + (6.2) 6.2 is the opposite of  6.2. Add 6.2 to both sides of the equation. a = 2.7 (2.7)  6.2 =  3.5 Solve a  6.2 =  3.5.

6. 6 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example Solve for c. 3c  8 = 2c  15 3c  8 + 8 = 2c  15 + 8 Add 8 to both sides of the equation. 3(  7)  8 = 2(  7)  15 3c = 2c  7 3c + (  2c) = 2c  7 + (  2c) Add  2c to both sides of the equation. c =  7  21  8 =  14  15  29 =  29 Check your answer in the original equation.

7. 7 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example Is 5 the solution of the equation –10 + 4 = x – 2? Solve for the solution. Thus, 5 is not the solution. Substitute 5 for x and see if we obtain an identity. –10 + 4 = x – 2 –10 + 4 = 5 – 2 –6 ≠ 3 –10 + 4 = x – 2 –6 = x – 2 –4 = x Check: Replacing x with –4 in the original equation, verifies the solution.

8. 8 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example Find the value of y that satisfies the equation The LCD is 10. Be sure to check your answer in the original equation. Add to both sides of the equation and simplify. Simplify.