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What is the solution for [tex]$x$[/tex] in the equation?

[tex]\frac{1}{2}-x+\frac{3}{2}=x-4[/tex]

A. [tex]$x=-3$[/tex]
B. [tex]$x=-\frac{1}{3}$[/tex]
C. [tex][tex]$x=3$[/tex][/tex]
D. [tex]$x=\frac{1}{3}$[/tex]


Sagot :

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]