Question

Which is the best description of the equivalency of the two expressions? Expression 1 Expression 2 5 x squared minus 2 x minus 4 + 6 x + 3 6 x squared minus 6 x + 6 minus x squared + 10 x minus 7 The two expressions are not equivalent because when x = 2, the two expressions do not have the same value. The two expressions are not equivalent because when they are simplified, they do not have the same coefficients for the x squared and x terms. They are equivalent because the sum of the constants is the same in both expressions. They are equivalent because when x = 2, the two expressions have the same value.

Answer 1

Answer:

The correct option is (D).

Step-by-step explanation:

The two expressions are:

$\text{Exp}_{1}=5x^{2}-2x-4+6x+3\\\\\text{Exp}_{2}=6x^{2}-6x+6-x^{2}+10x-7$

On simplifying both the expressions we get:

$\text{Exp}_{1}=5x^{2}+4x-1\\\\\text{Exp}_{2}=5x^{2}+4x-1$

Compute the value of both expressions for x = 2 as follows:

$\text{Exp}_{1}=5(2)^{2}+4(2)-1=27\\\\\text{Exp}_{2}=5(2)^{2}+4(2)-1=27$

The value of both expressions are same for x = 2.

Thus, the correct option is:

"They are equivalent because when x = 2, the two expressions have the same value."