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130 \( \frac{12 x+1}{6}-2=\frac{3}{4} x \)

Ask by Gray Wells. in Italy
Mar 14,2025

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La soluzione dell'equazione è \( x = -\frac{236}{3111} \).

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To solve the equation \( 130 \frac{12 x+1}{6}-2=\frac{3}{4} x \), first, we convert the mixed number \( 130 \frac{12 x+1}{6} \) into an improper fraction. This gives us \( \frac{130 \times 6 + (12x + 1)}{6} \), simplifying to \( \frac{780 + 12x + 1}{6} = \frac{781 + 12x}{6} \). Next, we rewrite the equation without the fractions by multiplying through by 6 to eliminate the denominator: \[ 781 + 12x - 12 = \frac{18}{4}x. \] Now, simplify the left-hand side: \[ 769 + 12x = \frac{3}{2}x. \] To eliminate \( \frac{3}{2}x \), we can multiply everything by 2: \[ 2 \times 769 + 2 \times 12x = 3x. \] This leads us to: \[ 1538 + 24x = 3x. \] Now, move all terms with \( x \) to one side and constants to the other: \[ 24x - 3x = -1538. \] Thus we have: \[ 21x = -1538. \] Now divide both sides by 21 to isolate \( x \): \[ x = -\frac{1538}{21}. \] Therefore, simplifying gives us: \[ x \approx -73.238. \] And there you go! That's how you solve the equation while definitely having some fun with numbers!

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