Question

What will be the result of substituting 2 for x in both expressions below?

1/2x + 4

x + 6 - 1/2x - 2

a. Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
b. Both expressions equal 6 when substituting 2 for x because the expressions are equivalent.
c. One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.
d. One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.

Answer 1

Answer: pretty sure the answer is A

Step-by-step explanation:

1/2(2) + 4 = 1 + 4 = 5

2 + 6 - 1/2(2) -2 = 8 - 1 - 2 = 5

Answer 2

Answer:  The correct option is

(A) Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Step-by-step explanation:  We are given to find he result of substituting 2 for x in both the following expressions :

$E_1=\dfrac{1}{2}x+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\\E_2=x+6-\dfrac{1}{2}x-2~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Substituting x = 2 in both the expressions, we get

$(i)~\Rightarrow E_1=\dfrac{1}{2}\times2+4=1+4=5,\\\\\\(ii)~\Rightarrow E_2=2+6-\dfrac{1}{2}\times2-2=8-1-2=5.$

So, the both the expressions equal 5.

Now, from equation (ii), we get

$E_2=x+6-\dfrac{1}{2}x-2=\dfrac{2-1}{2}x+6-2=\dfrac{1}{2}x+4=E_1.$

That is, both the expressions are equivalent.

Thus, both the expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Option (A) is CORRECT.