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

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=(1)/(2)x+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\\E_2=x+6-(1)/(2)x-2~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

Substituting x = 2 in both the expressions, we get

`(i)~\Rightarrow E_1=(1)/(2)*2+4=1+4=5,\\\\\\(ii)~\Rightarrow E_2=2+6-(1)/(2)*2-2=8-1-2=5.`

So, the both the expressions equal 5.

Now, from equation (ii), we get

`E_2=x+6-(1)/(2)x-2=(2-1)/(2)x+6-2=(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.