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.