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]
[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]