Nancy is checking to determine if the expressions x+4+x and 6+2x−2 are equivalent. When x=3, she correctly finds that both expressions have a value of 10. When x=5, she correctly evaluates the first expression to find that x+4+x=14. What is the value of the second expression when x is equal to 5 , and are the two expressions equivalent?
Answer
A
The value of the second expression is 8 , so the expressions are not equivalent.
B
The value of the second expression is 18 , so the expressions are not equivalent.
C
The value of the second expression is 16 , so the expressions are equivalent.
D
The value of the second expression is 14 , so the expressions are equivalent.
Explanation
Substitute x = 5 into the second expression: 6 + 2(5) − 2 = 6 + 10 − 2 = 14. The first expression also equals 14 when x = 5. In fact, both expressions simplify to 2x + 4, so they have the same value for every x and are equivalent. The correct choice is D: the second expression has a value of 14, and the expressions are equivalent.
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