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\( x=1 \)
Solución
Solve the equation \( \frac{2}{3}x-\frac{1}{2}=\frac{1}{6} \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{2}{3}x-\frac{1}{2}=\frac{1}{6}\)
- step1: Move the constant to the right side:
\(\frac{2}{3}x=\frac{1}{6}+\frac{1}{2}\)
- step2: Add the numbers:
\(\frac{2}{3}x=\frac{2}{3}\)
- step3: Multiply by the reciprocal:
\(\frac{2}{3}x\times \frac{3}{2}=\frac{2}{3}\times \frac{3}{2}\)
- step4: Multiply:
\(x=1\)
The solution to the equation \( \frac{2}{3}x-\frac{1}{2}=\frac{1}{6} \) is \( x=1 \).
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Simplifique esta solución Beyond the Answer
To solve the equation \( \frac{2}{3} x - \frac{1}{2} = \frac{1}{6} \), first, we need to eliminate the fractions for easier calculation. Multiply every term by 6 (the least common multiple of the denominators 3, 2, and 6): \[ 6 \left( \frac{2}{3} x \right) - 6 \left( \frac{1}{2} \right) = 6 \left( \frac{1}{6} \right) \] This simplifies to: \[ 4x - 3 = 1 \] Next, isolate \( x \) by adding 3 to both sides: \[ 4x = 4 \] Then, divide both sides by 4: \[ x = 1 \] So, the solution is \( x = 1 \). Now you’ve not only solved for \( x \), but you’ve also polished your algebra skills – high fives all around!
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