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

1 answer

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.