To solve the equation [tex]\(\frac{1}{2} - x + \frac{3}{2} = x - 4\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Combine like terms on the left-hand side of the equation:
The given equation is:
[tex]\[
\frac{1}{2} - x + \frac{3}{2} = x - 4
\][/tex]
Combine the constants [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
\left(\frac{1}{2} + \frac{3}{2}\right) - x = x - 4
\][/tex]
Adding the fractions gives:
[tex]\[
\frac{4}{2} - x = x - 4
\][/tex]
Simplify [tex]\(\frac{4}{2}\)[/tex]:
[tex]\[
2 - x = x - 4
\][/tex]
2. Move all terms involving [tex]\(x\)[/tex] to one side:
To isolate [tex]\(x\)[/tex], add [tex]\(x\)[/tex] to both sides of the equation:
[tex]\[
2 - x + x = x - 4 + x
\][/tex]
Simplify:
[tex]\[
2 = 2x - 4
\][/tex]
3. Isolate [tex]\(2x\)[/tex]:
Add 4 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
2 + 4 = 2x - 4 + 4
\][/tex]
Simplify:
[tex]\[
6 = 2x
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by 2:
[tex]\[
\frac{6}{2} = \frac{2x}{2}
\][/tex]
Simplify:
[tex]\[
3 = x
\][/tex]
Therefore, the solution is [tex]\(x = 3\)[/tex].
Hence, the correct answer is:
C. [tex]\(x = 3\)[/tex]
