Question

does 3/8x = 1 have the same solution as 1/3x = 1/8?

Answer 1

To determine if the equations \( \frac{3}{8}x = 1 \) and \( \frac{1}{3}x = \frac{1}{8} \) have the same solution, let's solve each equation step-by-step.

### Solving the first equation:

\[
\frac{3}{8}x = 1
\]

To solve for \( x \), multiply both sides by the reciprocal of \( \frac{3}{8} \), which is \( \frac{8}{3} \):

\[
x = 1 \cdot \frac{8}{3}
\]
\[
x = \frac{8}{3}
\]

### Solving the second equation:

\[
\frac{1}{3}x = \frac{1}{8}
\]

To solve for \( x \), multiply both sides by the reciprocal of \( \frac{1}{3} \), which is 3:

\[
x = \frac{1}{8} \cdot 3
\]
\[
x = \frac{3}{8}
\]

### Comparing the solutions:

- The solution to the first equation is \( x = \frac{8}{3} \).
- The solution to the second equation is \( x = \frac{3}{8} \).

Since \( \frac{8}{3} \) is not equal to \( \frac{3}{8} \), the two equations do not have the same solution.

### Conclusion:

The answer is no, \( \frac{3}{8}x = 1 \) does not have the same solution as \( \frac{1}{3}x = \frac{1}{8} \).