1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 8.2 Solving Linear Equations: ax + b = c

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Solve equations of the form ax + b = c.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Solving Equations of the Form ax + b = c Procedure for Solving Linear Equations that Simplify to the Form ax + b = c 1.Combine like terms on both sides of the equation. 2.Use the addition principle of equality and add the opposite of the constant b to both sides. 3. Use the multiplication (or division) principle of equality to multiply both sides by the reciprocal of the coefficient of the variable (or divide both sides by the coefficient itself). The coefficient of the variable will become  1.

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Solving Equations of the Form ax + b = c Procedure for Solving Linear Equations that Simplify to the Form ax + b = c (cont.) 4. Check your answer by substituting it for the variable in the original equation.

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Solving Linear Equations of the Form ax + b = c Solve the equation 3x + 3 =  18. Solution

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Solving Linear Equations of the Form ax + b = c (cont.) Check

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Solving Linear Equations of the Form ax + b = c Solve the equation –26 = 2y – 14 – 4y. Solution

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Solving Linear Equations of the Form ax + b = c (cont.) Check

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Solving Linear Equations involving Decimals Solve the equation 16.53 – 18.2z – 7.43 = 0. Solution

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Solving Linear Equations involving Decimals (cont.) Check

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Solving Linear Equations involving Decimals Solve the equation 5.1x + 7.4 – 1.8x = –9.1. Solution Because the decimal numbers are accurate to tenths, we could multiply both sides by 10 to get integer coefficients. However, we can also work with the decimal numbers directly as shown here.

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Solving Linear Equations involving Decimals (cont.) Check

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Solving Linear Equations with Fractional Coefficients Solve the equation Solution

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Solving Linear Equations with Fractional Coefficients (cont.)

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Solving Linear Equations with Fractional Coefficients (cont.) Check

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Solving Equations of the Form ax + b = c Notes About Checking: Checking can be quite time consuming and need not be done for every problem. This is particularly important on exams. You should check only if you have time after the entire exam is completed.

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Solving Linear Equations with Fractional Coefficients Solve the equation Solution

18. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Solving Linear Equations with Fractional Coefficients (cont.)

19. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Completion Example 7: Solving Linear Equations with Fractional Coefficients Solve the equation Solution

20. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Completion Example 7: Solving Linear Equations with Fractional Coefficients (cont.)

21. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Solve the following linear equations. 1. 2. 3. 4.

22. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1. 2. 3. 4.