Do you think each generalization is true for all interersa,b,c,&d? Substitute in

Question

Do you think each generalization is true for all interersa,b,c,&d? Substitute integers & find counter examplesif possible? a. (a+b)/c=a/c+b/c b. a/(b+c)=a/b+a/c c. (a+b) + (a-b)'a to the 2nd +b to the 2nd d. if a <b, then a to the 2nd <b to the 2nd e. if a<b, then c-a<c-b calculate the answers [-6+(-6)]+[-8+(-8)] [-12+(-18)](-16+-4) Do you think each generalization is true for all interersa,b,c,&d? Substitute integers & find counter examplesif possible? a. (a+b)/c=a/c+b/c b. a/(b+c)=a/b+a/c c. (a+b) + (a-b)'a to the 2nd +b to the 2nd d. if a <b, then a to the 2nd <b to the 2nd e. if a<b, then c-a<c-b calculate the answers [-6+(-6)]+[-8+(-8)] [-12+(-18)](-16+-4)

Explanation / Answer

a) Is True - this is based on adding fractions. b) Is not true. counter example would be:    Let a = 2          b = 3          c =4         2/(3+4) =2/7 for the left side                                  2/3+ 2/4 = 2/3 + 1/2 = 4/6 + 3/6 = 7/6 for the right side c) If you are adding (a + b) + (a-b) this would be 2a becausea + b + a - b d) Is not true. Counter example would be:    Let a = -3 and b = 2       -3<2 however (-3)(-3) =9 and (2)(2) = 4 so 9 is not less than 4 e) Is not true. Counter example would be:    Let a = -2, b = 1, and c = 3 -2<1 true however (3-(-2))= 5 and (3-1) = 2. Therefore 5 is not less than 2. [-6 +(-6)]+[-8+(-8)] = -12 +-16 = -28 [-12 +(-18)](-16 +-4) = (-28)(-20) = 560

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