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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

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Georgia Performance Standard Essential Question

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  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

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