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

C.
[tex]\[
\begin{array}{l}
4 = x + \frac{1}{2} \\
x = 3 \frac{1}{2}
\end{array}
\][/tex]

Answer :

We start with the statement that the sum of a number, [tex]$x$[/tex], and [tex]$\frac{1}{2}$[/tex] is equal to 4. This can be written as the equation

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

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

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

Since [tex]$4$[/tex] can be expressed as [tex]$\frac{8}{2}$[/tex], the equation becomes

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

Simplifying [tex]$\frac{7}{2}$[/tex] gives

[tex]$$
x = 3\frac{1}{2}.
$$[/tex]

Thus, the set of equations that correctly represents [tex]$x$[/tex] is

[tex]$$
\begin{array}{l}
4 = x + \frac{1}{2} \\
x = 3\frac{1}{2}
\end{array}
$$[/tex]

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