1 / 7

The Logic of Equation Solving

The Logic of Equation Solving. Lesson 3.4. Addition Property of Equality. Multiplication Property of Equality. f(x) = g(x) ↔ f(x) + h(x) = g(x) + h(x) If h ≠ 0, then, f(x) = g(x) ↔ f(x) • h(x) = g(x) • h(x). Example 1. Solve . Identify the property

jonas-suarez
Download Presentation

The Logic of Equation Solving

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. The Logic of Equation Solving Lesson 3.4

  2. Addition Property of Equality Multiplication Property of Equality f(x) = g(x) ↔ f(x) + h(x) = g(x) + h(x) If h ≠ 0, then, f(x) = g(x) ↔ f(x) • h(x) = g(x) • h(x)

  3. Example 1 Solve . Identify the property used to justify each step. Conclusion: Justification: x4-18 = 3(2x2+3) - mult. Prop. Of equ. x4-18 = 6x2+9 - distributive prop. x4- 6x2 -27 =0 - addition prop. (x2-9)(x2+3) = 0 - distributive prop x = 3, x = -3 - zero product. Check; both work!

  4. You try! -2(x2-8x+15) = 2x – 6 -mult. Prop. -2x2+16x-30 = 2x – 6 - dist. Prop. -2x2+14x -24 = 0 -add. Prop -2(x2-7x+12) = 0 -dist. Prop -2(x-3)(x-4) = 0 -dist. Prop x = 3, x = 4 -zero product. 3 doesn’t work!! x = 4

  5. Reversible steps vs. Irreversible • Reversible  they are bi-conditional (can be undone) • Irreversible  true conditional (if-then) statements for which the converse is false • Squaring both sides • Taking the log of both sides • Taking the square root of both sides • Multiplying out the denominator • If a function is 1-1, then the step is reversible. (x3, )

  6. Example 3 Find all real numbers x satisfying 32x-5 = 2187 Log32187 =2x-5 change to log Log2187/log3 =2x-5 change of base 7 = 2x – 5 12 = 2x addition x = 6 mult.

  7. Homework Pages 170 – 171 4-9, 11-15 20 - 24

More Related