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.
\[
\begin{array}{l}
4 = \frac{1}{2} x \\
x = 8
\end{array}
\]

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

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

D.
\[
\begin{array}{l}
4 = x + \frac{1}{2} \\
x = 4 \frac{1}{2}
\end{array}
\]

Answer :

We are given the equation

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

**Step 1.** Write the equation as:

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

**Step 2.** To isolate $x$, subtract $\frac{1}{2}$ from both sides:

$$
x = 4 - \frac{1}{2}.
$$

**Step 3.** Simplify the right-hand side:

$$
x = \frac{8}{2} - \frac{1}{2} = \frac{7}{2} = 3\frac{1}{2}.
$$

Thus, we have

$$
x = 3\frac{1}{2}.
$$

Among the provided sets, the correct representation is:

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

This set correctly represents the equation and the solution for $x$.

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