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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 ?

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 Dieg class=

Respuesta :

Answer:

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.

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