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Chris is checking to determine if the expressions [tex]2(x+3)[/tex] and [tex]2x+4+2x[/tex] are equivalent. When [tex]x=1[/tex], he correctly finds that both expressions have a value of 8. When [tex]x=2[/tex], he correctly evaluates the first expression to find that [tex]2(x+3)=10[/tex].

What is the value of the second expression when [tex]x=2[/tex], and are the two expressions equivalent?

A. The value of the second expression is 8, so the expressions are equivalent.
B. The value of the second expression is 10, so the expressions are equivalent.
C. The value of the second expression is 12, so the expressions are not equivalent.
D. The value of the second expression is 16, so the expressions are not equivalent.



Answer :

GinnyAnswer
To determine if the expressions [tex]\(2(x+3)\)[/tex] and [tex]\(2x+4+2x\)[/tex] are equivalent when [tex]\(x=2\)[/tex], we need to evaluate the second expression [tex]\(2x+4+2x\)[/tex]:

1. Start with the given value of [tex]\(x = 2\)[/tex].
2. Substitute [tex]\(x = 2\)[/tex] into the second expression:
[tex]\[ 2x + 4 + 2x = 2(2) + 4 + 2(2) \][/tex]
3. Perform the multiplications first:
[tex]\[ 2(2) + 4 + 2(2) = 4 + 4 + 4 = 4 + 4 + 4 \][/tex]
4. Add the terms together:
[tex]\[ 4 + 4 + 4 = 12 \][/tex]

Now we need to compare this result to the value of the first expression [tex]\(2(x+3)\)[/tex] when [tex]\(x=2\)[/tex]:
1. Substitute [tex]\(x = 2\)[/tex] into the first expression:
[tex]\[ 2(x+3) = 2(2+3) = 2(5) = 10 \][/tex]

Because the value of the second expression is 12 and the value of the first expression is 10, the two expressions are not equivalent.

Thus, the correct option is:
- The value of the second expression is 12, so the expressions are not equivalent.

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