College

Solve the equation using the distributive property:

[tex]
\[
\begin{array}{c}
\frac{1}{2}(x-14) + 11 = \frac{1}{2}x - (x-4) \\
\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - x + 4 \\
\frac{1}{2}x + 4 = -\frac{1}{2}x + 4
\end{array}
\]
[/tex]

When 4 is subtracted from both sides, the equation [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex] results. What is the value of [tex]\(x\)[/tex]?

A. [tex]\(-1\)[/tex]
B. [tex]\(-\frac{1}{2}\)[/tex]
C. [tex]\(0\)[/tex]
D. [tex]\(\frac{1}{2}\)[/tex]

Answer :

To solve the equation [tex]\(\frac{1}{2}(x-14)+11=\frac{1}{2}x-(x-4)\)[/tex], you should follow these steps:

1. Apply the Distributive Property:
- Distribute [tex]\(\frac{1}{2}\)[/tex] in [tex]\(\frac{1}{2}(x-14)\)[/tex], resulting in [tex]\(\frac{1}{2}x - 7\)[/tex].

2. Rewrite the Equation:
- Substitute back into the equation to get: [tex]\(\frac{1}{2}x - 7 + 11 = \frac{1}{2}x - (x - 4)\)[/tex].

3. Simplify Both Sides:
- On the left side, combine [tex]\(-7 + 11\)[/tex] to get [tex]\(4\)[/tex], so it becomes [tex]\(\frac{1}{2}x + 4\)[/tex].
- On the right side, distribute the negative sign, making it [tex]\(\frac{1}{2}x - x + 4\)[/tex].

4. Equating Both Sides:
- Write: [tex]\(\frac{1}{2}x + 4 = \frac{1}{2}x - x + 4\)[/tex].

5. Subtract 4 from Both Sides:
- Resulting equation: [tex]\(\frac{1}{2}x = -\frac{1}{2}x\)[/tex].

6. Solve for [tex]\(x\)[/tex]:
- Add [tex]\(\frac{1}{2}x\)[/tex] to both sides to combine like terms: [tex]\(\frac{1}{2}x + \frac{1}{2}x = 0\)[/tex].
- Simplify: [tex]\(x = 0\)[/tex].

Thus, the value of [tex]\(x\)[/tex] is 0.