Question

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 \(\boxed{-\frac{5}{2}}\).