Find the value of x in the following:
`1 2/3-:2/7xx x/7=1 1/4xx2/3-:1/6`

Options

A. 0.006
B. `1/6`
C. 0.6
D. 6

Answer

To solve the equation \( 1 \frac{2}{3} \div \frac{2}{7} \times \frac{x}{7} = 1 \frac{1}{4} \times \frac{2}{3} \div \frac{1}{6} \), we will follow these steps:

### Step 1: Convert mixed numbers to improper fractions
1. Convert \( 1 \frac{2}{3} \) to an improper fraction:
\[ 1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3} \]
2. Convert \( 1 \frac{1}{4} \) to an improper fraction:
\[ 1 \frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4} \]

### Step 2: Rewrite the equation
Now we can rewrite the equation:
\[ \frac{5}{3} \div \frac{2}{7} \times \frac{x}{7} = \frac{5}{4} \times \frac{2}{3} \div \frac{1}{6} \]

### Step 3: Simplify the left side
1. Change the division to multiplication by taking the reciprocal:
\[ \frac{5}{3} \times \frac{7}{2} \times \frac{x}{7} \]
2. The \( 7 \) in the numerator and denominator cancels out:
\[ \frac{5}{3} \times \frac{x}{2} \]

### Step 4: Simplify the right side
1. Change the division to multiplication by taking the reciprocal:
\[ \frac{5}{4} \times \frac{2}{3} \times 6 \]
2. Simplify \( \frac{2}{3} \div \frac{1}{6} \):
\[ \frac{2}{3} \times 6 = \frac{2 \times 6}{3} = \frac{12}{3} = 4 \]
3. Now multiply:
\[ \frac{5}{4} \times 4 = 5 \]

### Step 5: Set the equations equal
Now we have:
\[ \frac{5}{3} \times \frac{x}{2} = 5 \]

### Step 6: Solve for \( x \)
1. Multiply both sides by \( 2 \):
\[ \frac{5}{3} x = 10 \]
2. Multiply both sides by \( \frac{3}{5} \):
\[ x = 10 \times \frac{3}{5} = 6 \]

### Final Answer
The value of \( x \) is \( 6 \).

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