4. Tanya has the equation x - 2 = 2x - 4. She states that adding x + 2 to both sides will keep the solution set the same because of the additive property of equality. Diego states that you could
also multiply both sides of Tanya's equation by x+2 and have the same solution set because of
the multiplicative property of equality.
a) is tanyas statement correct?
b)is diego’s statement correct ?

Tanya is correct.

Step-by-step explanation:

a). Tanya has the equation,

   x - 2 = 2x - 4

   x - 2x = 2 - 4

  -x = -2

   x = 2

  By adding (x + 2) on both the sides of the equation,

  (x - 2) + (x + 2) = (2x - 4) + (x + 2)

  2x = 3x - 2

  2x - 3x = -2

  x = 2

Tanya is correct.

b). By Diego's statement

   (x - 2)(x + 2) = (2x - 4)(x + 2)

   x² - 4 = 2x²- 8

   x² - 2x² = 4 - 8

   -x² = -4

    x² = 4

    x = ±2

 Therefore, Diego's statement is incorrect.

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!