Downloaded 34 times
More Related Content
Similar to Lesson 3 solving linear & quadratic equations
Lesson 3 solving linear & quadratic equations
- 1. MATH 107 Section 1.1& 1.4 Solving Linear & Quadratic Equations
- 4. PROCEDURE FOR SOLVINGLINEAR EQUATIONS IN ONE VARIABLE Step 1 Eliminate Fractions. Multiply both sides of the equation by the least common denominator (LCD) of all the fractions. Step 2 Simplify. Simplify both sides of the equation by removing parentheses and other grouping symbols (if any) and combining like terms. © 2010 Pearson Education, Inc. All rights reserved 4
- 5. PROCEDURE FOR SOLVINGLINEAR EQUATIONS IN ONE VARIABLE Step 3 Isolate the Variable Term. Add appropriate expressions to both sides, so that when both sides are simplified, the terms containing the variable are on one side and all constant terms are on the other side. Step 4 Combine Terms. Combine terms containing the variable to obtain one term that contains the variable as a factor. © 2010 Pearson Education, Inc. All rights reserved 5
- 6. PROCEDURE FOR SOLVINGLINEAR EQUATIONS IN ONE VARIABLE Step 5 Isolate the Variable. Divide both sides by the coefficient of the variable to obtain the solution. Step 6 Check the Solution. Substitute the solution into the original equation. © 2010 Pearson Education, Inc. All rights reserved 6
- 7. Solve the equation:4 7 13x − =
- 8. ( ) () 1 1 Solve the equation: 1 3 3 2 3 4 x x− − = +
- 9. ( ) () ( ) ( )Solve the equation: 3 1 2 3 3 2x x x x− + = + −
- 10. ( ) () 2 3 1 Solve the equation: 1 3 3 1x x x x = + − + + −
- 11. 3 6 Solve theequation: 1 2 2 x x x + = − −
- 12. ( ) In theUnited States we measure temperature in both degrees Fahrenheit ( F) and degrees Celsius ( C). 5 They are related by the formula 32 . 9 What are the Fahrenheit temperatures corresponding to Cel C F ° ° = − sius temperatures of 10 ,0 ,and 40 ?− ° ° °
- 13.
- 14. A total of$16,000 is invested, some in stocks and some in bonds. If the amount invested in bonds is one fourth that invested in stocks, how much is invested in each category? We are being asked to find the amount of two investments. These amounts total $16,000.
- 15. A total of$16,000 is invested, some in stocks and some in bonds. If the amount invested in bonds is one fourth that invested in stocks, how much is invested in each category? If x equals the amount invested in stocks, then the rest of the money, 16,000 – x, is the amount invested in bonds.
- 16. A total of$16,000 is invested, some in stocks and some in bonds. If the amount invested in bonds is one fourth that invested in stocks, how much is invested in each category?
- 17. A total of$16,000 is invested, some in stocks and some in bonds. If the amount invested in bonds is one fourth that invested in stocks, how much is invested in each category?
- 18. A total of$16,000 is invested, some in stocks and some in bonds. If the amount invested in bonds is one fourth that invested in stocks, how much is invested in each category?
- 19. Andy grossed $440one week by working 50 hours. His employer pays time-and-a-half for all hours worked in excess of 40 hours. What is Andy’s hourly wage? We are looking for an hourly wage. Our answer will be expressed in dollars per hour.
- 20. Andy grossed $440one week by working 50 hours. His employer pays time-and-a-half for all hours worked in excess of 40 hours. What is Andy’s hourly wage?
- 21. Andy grossed $440one week by working 50 hours. His employer pays time-and-a-half for all hours worked in excess of 40 hours. What is Andy’s hourly wage?
- 22. Andy grossed $440one week by working 50 hours. His employer pays time-and-a-half for all hours worked in excess of 40 hours. What is Andy’s hourly wage?
- 23. Andy grossed $440one week by working 50 hours. His employer pays time-and-a-half for all hours worked in excess of 40 hours. What is Andy’s hourly wage?
- 24. QUADRATIC EQUATION A quadraticequation in the variable x is an equation equivalent to the equation where a, b, and c are real numbers and a ≠ 0. ax2 + bx + c = 0, © 2010 Pearson Education, Inc. All rights reserved 24
- 25. THE ZERO-PRODUCT PROPERTY Let Aand B be two algebraic expressions. Then AB = 0 if and only if A = 0 or B = 0. © 2010 Pearson Education, Inc. All rights reserved 25
- 26. Step 1 Writethe given equation in standard form so that one side is 0. Step 2 Factor the nonzero side of the equation. Step 3 Set each factor to 0. Step 4 Solve the resulting equations. SOLVING A QUADRATIC EQUATION BY FACTORING Step 5 Check the solutions in original equation © 2010 Pearson Education, Inc. All rights reserved 26
- 27. EXAMPLE 1 Solvinga Quadratic Equation by Factoring. Solve by factoring: 2x2 +5x = 3. © 2010 Pearson Education, Inc. All rights reserved 27
- 28. EXAMPLE 2 Solvinga Quadratic Equation by Factoring. Solve by factoring: 2 3 2 .t t= © 2010 Pearson Education, Inc. All rights reserved 28
- 29. EXAMPLE 3 Solvinga Quadratic Equation by Factoring. Solve by factoring: 2 16 8 .x x+ = © 2010 Pearson Education, Inc. All rights reserved 29
- 30. Suppose u isany algebraic expression and d ≥ 0. THE SQUARE ROOT PROPERTY If u2 = d, then u = ± d. © 2010 Pearson Education, Inc. All rights reserved 30
- 31. EXAMPLE 4 Solvingan Equation by the Square Root Method Solve: ( ) 2 3 5.x − = © 2010 Pearson Education, Inc. All rights reserved 31
- 32. The solutions ofthe quadratic equation in the standard form ax2 + bx + c = 0 with a ≠ 0 are given by the formula THE QUADRATIC FORMULA 2 4 . 2 b b ac x a − ± − = © 2010 Pearson Education, Inc. All rights reserved 32
- 33. EXAMPLE 7 Solving aQuadratic Equation by Using the Quadratic Formula Solve by using the quadratic formula. 2 3 5 2x x= + Solution © 2010 Pearson Education, Inc. All rights reserved 33
- 34. EXAMPLE 10 Partitioninga Building A rectangular building whose depth (from the front of the building) is three times its frontage is divided into two parts by a partition that is 45 feet from and parallel to the front wall. Assuming the rear portion of the building contains 2100 square feet, find the dimensions of the building. Solution © 2010 Pearson Education, Inc. All rights reserved 34