1/3x + 1 = 1/6 What is the value of x?

Answer 1

To solve the equation \( \frac{1}{3}x + 1 = \frac{1}{6} \), we will first isolate \( x \).

1. Start by subtracting 1 from both sides: \[ \frac{1}{3}x = \frac{1}{6} - 1 \]

2. Convert 1 to a fraction with a denominator of 6: \[ 1 = \frac{6}{6} \]

3. Now subtract: \[ \frac{1}{6} - \frac{6}{6} = \frac{1 - 6}{6} = \frac{-5}{6} \]

4. Now we have: \[ \frac{1}{3}x = \frac{-5}{6} \]

5. To solve for \( x \), multiply both sides by the reciprocal of \( \frac{1}{3} \), which is 3: \[ x = 3 \times \frac{-5}{6} \]

6. Simplify: \[ x = \frac{3 \times -5}{6} = \frac{-15}{6} \]

7. Reduce the fraction: \[ x = \frac{-15 \div 3}{6 \div 3} = \frac{-5}{2} \]

Thus, the value of \( x \) is \(\boxed{-\frac{5}{2}}\).