Algebraic proofs

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Intros
Lessons
  1. Algebraic Proofs Overview:
  2. Properties of Equality for Real Numbers
  3. Two-Column Proof Example
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Examples
Lessons
  1. Understanding the Properties of Equality
    State which property was used in each statement:
    1. If y2=3\frac{y}{2}=3 , then y=6y=6 .
    2. a=aa=a
    3. If 2x+3=52x+3=5, then 2x=22x=2.
    4. If 3(5x+1)=23(5x+1)=2, then 15x+3=215x+3=2
    5. If ac=bcac=bc , then a=ba=b .
    6. If x=8x=8 and 8=y8=y , then x=yx=y .
  2. If 3a=3b3a=3b , then which property is used to justify that a=ba=b ?
    1. If 3(a+b)=73(a+b)=7 , then which property is used to justify that 3=7a+b3=\frac{7}{a+b} ?
      1. Two Column Proofs
        Prove that if 2(4x+1)=102(4x+1)=10 , then x=1x=1 . Use the two column-proof method
        1. Prove that if 15=2(x+5)+3x515=2(x+5)+3x-5 , then x=2x=2 . Use the two column-proof method.
          1. Prove that if y3+3y4=6 \frac{y}{3} +3y-4=6 , then y=3y=3 . Use the two column-proof method.