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What will be the result of substituting 2 for [tex]$x$[/tex] in both expressions below?

[tex]\[
\begin{array}{l}
\frac{1}{2} x + 4 \\
x + 6 - \frac{1}{2} x - 2
\end{array}
\][/tex]

A. Both expressions equal 5 when substituting 2 for [tex]$x$[/tex] because the expressions are equivalent.

B. Both expressions equal 6 when substituting 2 for [tex]$x$[/tex] because the expressions are equivalent.

C. One expression equals 5 when substituting 2 for [tex]$x$[/tex], and the other equals 2 because the expressions are not equivalent.

D. One expression equals 6 when substituting 2 for [tex]$x$[/tex], and the other equals 2 because the expressions are not equivalent.



Answer :

GinnyAnswer
Let's solve this problem step by step.

To find the result of substituting \( x = 2 \) into each given expression, we will evaluate each expression separately.

### First expression:
[tex]\[ \frac{1}{2} x + 4 \][/tex]

1. Substitute \( x = 2 \):
[tex]\[ \frac{1}{2} \times 2 + 4 \][/tex]

2. Simplify the multiplication:
[tex]\[ \frac{2}{2} + 4 \][/tex]

3. \(\frac{2}{2}\) simplifies to 1:
[tex]\[ 1 + 4 \][/tex]

4. Add the terms:
[tex]\[ 1 + 4 = 5 \][/tex]

So, the first expression equals 5 when \( x = 2 \).

### Second expression:
[tex]\[ x + 6 - \frac{1}{2} x - 2 \][/tex]

1. Substitute \( x = 2 \):
[tex]\[ 2 + 6 - \frac{1}{2} \times 2 - 2 \][/tex]

2. Simplify the multiplication:
[tex]\[ 2 + 6 - 1 - 2 \][/tex]

3. Combine like terms:
[tex]\[ 2 + 6 - 1 - 2 = 8 - 1 - 2 \][/tex]

4. Continue combining:
[tex]\[ 8 - 1 = 7 \][/tex]
[tex]\[ 7 - 2 = 5 \][/tex]

So, the second expression also equals 5 when \( x = 2 \).

### Conclusion
Both expressions evaluate to 5 when substituting \( x = 2 \). Therefore, the correct answer is:

Both expressions equal 5 when substituting 2 for [tex]\( x \)[/tex] because the expressions are equivalent.

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