1 / 12

Warm-up

Warm-up. Solve the following equations and show each step. 5x – 18 = 3x + 2 2) 55z – 3(9z+12)= – 64 2x – 18 = 2 2x = 20 x = 10. 55z – 27z – 36 = – 64 28z – 36 = – 64 28z = – 28 z = – 1. Reasoning with Properties of Equality. Objectives.

ralph-adams
Download Presentation

Warm-up

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. Warm-up • Solve the following equations and show each step. • 5x – 18 = 3x + 2 2) 55z – 3(9z+12)= – 64 2x – 18 = 2 2x = 20 x = 10 55z – 27z – 36 = – 64 28z – 36 = – 64 28z = – 28 z = – 1

  2. Reasoning with Properties of Equality

  3. Objectives • I can write a statement with proper notation. • I can judge if an argument has enough evidence to be true. • I can sequence my statements logically. What we will do today lays the groundwork for: • I can write a two-column proof.

  4. Algebraic Properties of Equality Let a, b, and c be real numbers. Addition Property of Equality: If a = b, then a + c = b + c Abbr. Add. Prop. of = Subtraction Property of Equality: If a = b, then a - c = b - c Abbr. Subt. Prop. of = Multiplication Property of Equality: If a = b, then ac = bc Abbr. Mult. Prop. of = Division Property of Equality: If a = b and c ≠ 0, then a/c = b/c Abbr. Div. Prop. of =

  5. Algebraic Properties of Equalitycontinued… Reflexive Property: For any real number a, a = a Abbr. Refl. Prop. of = Symmetric Property: If a = b, then b= a Abbr. Sym. Prop. of = Transitive Property: If a = b and b=c , then a =c Abbr. Trans. Prop. of = Substitution Property: If a = b, thena can be substituted for b in any equation or expression. Abbr. Subs. Prop. of =

  6. Use properties to support your argument. • All the algebraic properties of equality can be used to solve equation. • Other properties, such as the distributive property can also be used. a( b + c ) = ab+ ac Abbr. Distrib. Prop.

  7. Two-Column Proof Statements Reasons A definition, property, postulate or theorem that proves or explains why the statement is true. Reason 1 is always “Given” Property,etc. that explains the change from the previous step to this one. Same as Reason 2. Usually written in symbols and mathematical notation. • Statement 1 • Statement 2 • Last statement is what you wanted to prove.

  8. Given p – 1 = 6, prove that p = 7. Statements Reasons A definition, property, postulate or theorem that proves or explains why the statement is true. Given Addition Prop. of Equality Usually written in symbols and mathematical notation. • p - 1 =6 • p = 7

  9. Given 2r – 7 = 9, prove that r = 8. Statements Reasons A definition, property, postulate or theorem that proves or explains why the statement is true. Given Addition Prop. of Equality Division Prop. of Equality Usually written in symbols and mathematical notation. • 2r – 7 = 9 • 2r = 16 • r = 8

  10. Solve 3(2t + 9) = 30 and state the reason for each step. Statements Reasons Given Distrib. Prop. Subt. Prop. of = Div. Prop of = • 3(2t + 9) = 30 • 6t + 27 = 30 • 6t = 3 • t = 0.5

  11. Solve 3(2t + 9) = 30 and state the reason for each step. Statements Reasons Given Div. Prop. of = Subt. Prop. of = Div. Prop of = • 3(2t + 9) = 30 • 2t + 9 = 10 • 2t = 1 • t = 0.5

  12. Solve 3(4v – 1) – 8v = 17 and state the reason for each step. Statements Reasons Given Distrib. Prop. Combine Like Terms Add. Prop of = Div. Prop of = • 3(4v – 1) – 8v = 17 • 12v – 3 – 8v = 17 • 4v – 3 = 17 • 4v = 20 • v = 5

More Related