Question

does x/-3.2x=1.8 have the same answer as 1.8x=3.2?

Answer 1

To determine whether the equations \( \frac{x}{-3.2x} = 1.8 \) and \( 1.8x = 3.2 \) have the same solution, we can solve each equation separately.

### Solving the first equation:
Starting with the equation:

\[
\frac{x}{-3.2x} = 1.8
\]

Assuming \( x \neq 0 \), we can simplify \( \frac{x}{-3.2x} \):

\[
\frac{1}{-3.2} = 1.8
\]

Now, we can multiply both sides by \(-3.2\):

\[
1 = 1.8 \times (-3.2)
\]

Calculating \( 1.8 \times (-3.2) \):

\[
1.8 \times -3.2 = -5.76
\]

Thus:

\[
1 = -5.76
\]

This statement is incorrect, indicating that there are no solutions to the first equation.

### Solving the second equation:
Now let’s solve the second equation:

\[
1.8x = 3.2
\]

To solve for \( x \), divide both sides by \( 1.8 \):

\[
x = \frac{3.2}{1.8}
\]

Calculating \( \frac{3.2}{1.8} \):

\[
x \approx 1.7778 \quad (\text{or } \frac{16}{9})
\]

### Conclusion:
- The first equation \( \frac{x}{-3.2x} = 1.8 \) has no solutions.
- The second equation \( 1.8x = 3.2 \) has a solution \( x \approx 1.7778 \).

Therefore, the two equations do **not** have the same answer.