Question

Randy is checking to determine if the expressions 2x+2+4x and 2(3x+1) are equivalent. When x=3, he correctly finds that both expressions have a value of 20. When x=2, he correctly evaluates the first expression to find that 2x+2+4x=14.What is the value of the second expression when x=2 and are the two expressions equivalent?
A. The value of the second expression is 7, so the expressions are not equivalent.
B. The value of the second expression is 12, so the expressions are not equivalent.
C. The value of the second expression is 14, so the expressions are equivalent.
D. The value of the second expression is 20, so the expressions are equivalent.

Answer 1

Answer:

the correct answer is C

Answer 2

We have that
2x+2+4x---------> expression A
and 
2(3x+1)----------> expression B

expression A=2x+2+4x--------> (2x+4x)+2----------> 6x+2
expression A=6x+2

expression B=2(3x+1)------> 2*3x+2*1---------> 6x+2
expression B=6x+2

therefore
expression A=expression B------------> the two expressions are equivalent

so
if the expression A for x=2 is 14
the expression B for x=2 also is 14

the answer Part  A)
the value of the second expression when x=2 is 14

the answer Part B) the two expressions are equivalent

let's check it
for x=2
expression B=6x+2--------> 6*2+2-----> 14

 the answer is the option C.)
The value of the second expression is 14, so the expressions are equivalent.