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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]
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]
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