1 / 21

Georgia Performance Standard Essential Question

Georgia Performance Standard Essential Question. MM1A3 Students will solve simple equations. b. Solve equations involving radicals such as √x + b = c using algebraic techniques. Essential Question: How do you solve equations including radicals such as √x + b = c?. Activating Strategy

lahela
Télécharger la présentation

Georgia Performance Standard Essential Question

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Georgia Performance Standard Essential Question • MM1A3Students will solve simple equations. • b. Solve equations involving radicals such as √x + b = c using algebraic techniques. • Essential Question:How do you solve equations including radicals such as √x + b = c?

  2. Activating Strategy • Solve each equation. • 1. 3x +5 = 17 • 2. 4x + 1 = 2x – 3 • 3. • 4. (x + 7)(x – 4) = 0 • 5. x2 – 11x + 30 = 0 • 6.x2 = 2x + 15 4 –2 35 –7, 4 6, 5 5, –3

  3. Objective Solve radical equations.

  4. Vocabulary radical equation extraneous solution

  5. Check 5 5 5 Example 1A: Solving Simple Radical Equations Solve the equation. Check your answer. Square both sides. x = 25 Substitute 25 for x in the original equation.  Simplify.

  6. Check 10 10 Example 1B: Solving Simple Radical Equations Solve the equation. Check your answer. Square both sides. 100 = 2x 50 = x Divide both sides by 2. Substitute 50 for x in the original equation.  Simplify.

  7. Check Example 2A: Solving Simple Radical Equations Solve the equation. Check your answer. Add 4 to both sides. Square both sides. x = 81 9 – 4 5  5 5

  8. Check  7 7 Example 2B: Solving Simple Radical Equations Solve the equation. Check your answer. Square both sides. x = 46 Subtract 3 from both sides.

  9. Example 2C: Solving Simple Radical Equations Solve the equation. Check your answer. Subtract 6 from both sides. Square both sides. 5x + 1 = 16 5x = 15 Subtract 1 from both sides. x = 3 Divide both sides by 5.

  10. Example 3A: Solving Radical Equations by Multiplying or Dividing Solve the equation. Check your answer. Divide both sides by 4. Square both sides. x = 64

  11. Example 3B: Solving Radical Equations by Multiplying or Dividing Solve the equation. Check your answer. Multiply both sides by 2. Square both sides. 144 = x

  12. Check It Out! Example 3c Solve the equation. Check your answer. Multiply both sides by 5. Square both sides. Divide both sides by 4. x = 100

  13. Check Example 4A: Solving Radical Equations with Square Roots on Both Sides Solve the equation. Check your answer. Square both sides. 2x –1 = x + 7 Add 1 to both sides and subtract x from both sides. x = 8 

  14. Squaring both sides of an equation may result in an extraneous solution—a number that is not a solution of the original equation. Suppose your original equation is x = 3. x = 3 x2 = 9 Square both sides. Now you have a new equation. Solve this new equation for x by taking the square root of both sides. x = 3 or x = –3

  15. Now there are two solutions. One (x = 3) is the original equation. The other (x = –3) is extraneous–it is not a solution of the original equation. Because of extraneous solutions, it is important to check your answers.

  16. Example 5A: Extraneous Solutions Solve Check your answer. Subtract 12 from each sides. Square both sides 6x = 36 Divide both sides by 6. x = 6

  17. Check Example 5A Continued Solve Check your answer. Substitute 6 for x in the equation.  18 6 6 does not check. There is no solution.

  18. Check It Out! Example 5c Solve the equation. Check your answer. Square both sides x2– 5x +4 = 0 Write in standard form. (x– 1)(x– 4) = 0 Factor. X– 1 = 0 or x– 4 = 0 Zero-Product Property. x = 1 or x = 4 Solve for x.

  19. Check   2 2 Check It Out! Example 5c Continued Solve the equation. Check your answer. Substitute 1 for x in the equation. Substitute 4 for x in the equation. 1 does not check; it is extraneous. The only solution is 4.

  20. Key Points to Remember • Always make sure the radical is isolated. • Use inverse operations to isolate the radical. • Make sure to square both sides to get rid of the radical. • Remember to always check your work for extraneous solutions.

  21. Lesson Quiz (TOD) Solve each equation. Check your answer. 1. 2. 36 45 no solution 3. 4. 11

More Related