High School

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The sum of a number, [tex]x[/tex], and [tex]\frac{1}{2}[/tex] is equal to 4. Which set of equations correctly represents [tex]x[/tex]?

A.
[tex]\[

\begin{array}{l}

4=\frac{1}{2} x \\

x=8

\end{array}

\][/tex]

B.
[tex]\[

\begin{array}{l}

4=\frac{1}{2} x \\

x=2

\end{array}

\][/tex]

C.
[tex]\[

4 = x + \frac{1}{2}

\][/tex]

D.
[tex]\[

x = 3 \frac{1}{2}

\][/tex]

E.
[tex]\[

x = 4 \frac{1}{2}

\][/tex]

Answer :

We start with the equation given by the problem:

[tex]$$
x + \frac{1}{2} = 4.
$$[/tex]

To isolate [tex]\( x \)[/tex], subtract [tex]\(\frac{1}{2}\)[/tex] from both sides:

[tex]$$
x = 4 - \frac{1}{2}.
$$[/tex]

Calculating [tex]\(4 - \frac{1}{2}\)[/tex]:

[tex]$$
4 - \frac{1}{2} = \frac{8}{2} - \frac{1}{2} = \frac{7}{2} = 3\frac{1}{2}.
$$[/tex]

Thus, [tex]\( x = 3\frac{1}{2} \)[/tex].

The set of equations that correctly represents [tex]\( x \)[/tex] is:

[tex]$$
4 = x + \frac{1}{2} \quad \text{and} \quad x = 3\frac{1}{2}.
$$[/tex]

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