Question

1/3x + 1 = 1/6 What is the value of x? (2x + 3)

Answer 1

To solve the equation \( \frac{1}{3}x + 1 = \frac{1}{6} \), we 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:
\[
1 = \frac{6}{6}
\]
Therefore,
\[
\frac{1}{6} - \frac{6}{6} = \frac{1 - 6}{6} = \frac{-5}{6}
\]
Now we have:
\[
\frac{1}{3}x = \frac{-5}{6}
\]

3. To solve for \( x \), multiply both sides by the reciprocal of \( \frac{1}{3} \), which is 3:
\[
x = 3 \cdot \frac{-5}{6}
\]
This simplifies to:
\[
x = \frac{-15}{6} = \frac{-5}{2}
\]

Now, we want to find the value of \( 2x + 3 \):

4. Substitute \( x = \frac{-5}{2} \) into \( 2x + 3 \):
\[
2x + 3 = 2 \left(\frac{-5}{2}\right) + 3
\]
Simplifying this gives:
\[
2x + 3 = -5 + 3 = -2
\]

The final answer is:
\[
\boxed{-2}
\]