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Solve for \( x \):
[tex]\[ \frac{x-7}{3} = \frac{x-1}{3} \][/tex]


Sagot :

Sure! Let's solve the given equation step-by-step:

1. Understand the equation: The given equation is:
[tex]\[ \frac{x-7}{3} = \frac{x-1}{3} \][/tex]

2. Eliminate the denominators: Since the denominators on both sides are equal, we can eliminate the fractions by multiplying both sides of the equation by 3:
[tex]\[ 3 \cdot \frac{x-7}{3} = 3 \cdot \frac{x-1}{3} \][/tex]
This simplifies to:
[tex]\[ x-7 = x-1 \][/tex]

3. Isolate the variable: To isolate \(x\), first, we subtract \(x\) from both sides of the equation:
[tex]\[ (x - 7) - x = (x - 1) - x \][/tex]
Simplifying this yields:
[tex]\[ -7 = -1 \][/tex]

4. Analyze the result: The equation \(-7 = -1\) is a false statement. This implies that no value of \(x\) can satisfy the original equation.

Therefore, the equation [tex]\(\frac{x-7}{3} = \frac{x-1}{3}\)[/tex] has no solution.