Pregunta
2. \( \frac{x-1}{2}-\frac{x-2}{3}-\frac{x-3}{4}=5 \)
Ask by Paul Knight. in South Africa
Feb 10,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( x = -49 \)
Solución
Solve the equation \( \frac{x-1}{2}-\frac{x-2}{3}-\frac{x-3}{4}=5 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{x-1}{2}-\frac{x-2}{3}-\frac{x-3}{4}=5\)
- step1: Multiply both sides of the equation by LCD:
\(\left(\frac{x-1}{2}-\frac{x-2}{3}-\frac{x-3}{4}\right)\times 12=5\times 12\)
- step2: Simplify the equation:
\(-x+11=60\)
- step3: Move the constant to the right side:
\(-x=60-11\)
- step4: Subtract the numbers:
\(-x=49\)
- step5: Change the signs:
\(x=-49\)
The solution to the equation \( \frac{x-1}{2}-\frac{x-2}{3}-\frac{x-3}{4}=5 \) is \( x = -49 \).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
To solve the equation \( \frac{x-1}{2}-\frac{x-2}{3}-\frac{x-3}{4}=5 \), we first find a common denominator, which in this case is 12. Rewriting the equation with this common denominator gives us: \[ 6(x - 1) - 4(x - 2) - 3(x - 3) = 60 \] Distributing gives: \[ 6x - 6 - 4x + 8 - 3x + 9 = 60 \] Combining like terms, we have: \[ (6x - 4x - 3x) + (-6 + 8 + 9) = 60 \] \[ -x + 11 = 60 \] Now, to isolate \( x \), we subtract 11 from both sides: \[ -x = 49 \] Multiplying by -1 gives: \[ x = -49 \] So, the solution to the equation is \( x = -49 \).
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