Question

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 ?

Answer 1

Tanya is correct.

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.