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La solución de la ecuación es \( x=-4 \).
Solución
Solve the equation \( \frac{x}{6}+5=\frac{1}{3}-x \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{x}{6}+5=\frac{1}{3}-x\)
- step1: Multiply both sides of the equation by LCD:
\(\left(\frac{x}{6}+5\right)\times 6=\left(\frac{1}{3}-x\right)\times 6\)
- step2: Simplify the equation:
\(x+30=2-6x\)
- step3: Move the variable to the left side:
\(x+30+6x=2\)
- step4: Add the terms:
\(7x+30=2\)
- step5: Move the constant to the right side:
\(7x=2-30\)
- step6: Subtract the numbers:
\(7x=-28\)
- step7: Divide both sides:
\(\frac{7x}{7}=\frac{-28}{7}\)
- step8: Divide the numbers:
\(x=-4\)
La solución de la ecuación \( \frac{x}{6}+5=\frac{1}{3}-x \) es \( x=-4 \).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Extra Insights
To solve the equation \( \frac{x}{6}+5=\frac{1}{3}-x \), first, let's eliminate the fractions by finding a common denominator, which is 6. Multiplying each term by 6 gives us: \[ 6 \left( \frac{x}{6} \right) + 6(5) = 6 \left( \frac{1}{3} \right) - 6(x) \] This simplifies to: \[ x + 30 = 2 - 6x \] Now, let's get all the \(x\) terms on one side by adding \(6x\) to both sides: \[ x + 6x + 30 = 2 \] This simplifies to: \[ 7x + 30 = 2 \] Next, we isolate \(7x\) by subtracting 30 from both sides: \[ 7x = 2 - 30 \] This becomes: \[ 7x = -28 \] Now, divide by 7 to solve for \(x\): \[ x = -4 \] So, the solution to the equation is \( x = -4 \).
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