1 over 3 equals 4 over x minus 1 over 6 solve and answer

We have the equation:

\[
\frac{1}{3} = \frac{4}{x} - \frac{1}{6}
\]

To solve for \( x \), let's follow these steps:

### Step 1: Eliminate the fractions by finding a common denominator.
The denominators are 3, \( x \), and 6. The common denominator between 3 and 6 is 6, and \( x \) will be included separately.

Multiply every term by 6x:

\[
6x \cdot \frac{1}{3} = 6x \cdot \frac{4}{x} - 6x \cdot \frac{1}{6}
\]

This simplifies to:

\[
2x = 24 - x
\]

### Step 2: Solve the equation for \( x \).
Add \( x \) to both sides to get:

\[
2x + x = 24
\]

\[
3x = 24
\]

Divide by 3:

\[
x = 8
\]

### Final Answer:
The solution is \( x = 8 \).

Would you like more details or have any questions? 

Here are 5 related questions for further practice:
1. Solve \(\frac{2}{5} = \frac{7}{y} - \frac{1}{10}\).
2. What is the solution for \( \frac{5}{x} + \frac{2}{3} = \frac{7}{6} \)?
3. Solve \( \frac{3}{4} = \frac{5}{y} - \frac{2}{8} \).
4. Find \( x \) if \( \frac{1}{x} = \frac{2}{7} + \frac{1}{14} \).
5. Determine the value of \( x \) in \( \frac{1}{x} + \frac{1}{3} = \frac{5}{6} \).

**Tip:** When dealing with equations involving fractions, it's often helpful to multiply through by the least common denominator (LCD) to eliminate the fractions right away.

Learn how to solve the equation 1/3 = 4/x - 1/6 with a step-by-step solution. This problem involves fractions and algebraic manipulation. Suitable for students in Grades 7-9.

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