Which of the following pairs of equations has exactly the same solution?(1 point)

Question

Responses

−34x=52
and 52x=−34
negative Start Fraction 3 over 4 End Fraction x equals Start Fraction 5 over 2 End Fraction and Start Fraction 5 over 2 End Fraction x equals negative Start Fraction 3 over 4 End Fraction

x3.2=1.8
and 1.8x=3.2
Start Fraction x over 3.2 End Fraction equals 1.8 and 1.8x equals 3.2

−3.2x=0.64
and x4=−0.05
negative 3.2x equals 0.64 and Start Fraction x over 4 End Fraction equals negative 0.05

38x=1
and 13x=18

Answer 1

To determine which pairs of equations have exactly the same solution, we can solve each pair and analyze the results. Let's evaluate each pair:

1. −34x = 52 and 52x = −34:

   For the first equation, solve for x: \[ x = \frac{52}{-34} = -\frac{26}{17} \]

   For the second equation: \[ x = \frac{-34}{52} = -\frac{17}{26} \] These solutions are not the same.

2. −\(\frac{3}{4}\) x = \(\frac{5}{2}\) and \(\frac{5}{2}\) x = −\(\frac{3}{4}\):

   For the first equation: \[ x = \frac{5}{2} \cdot \left(-\frac{4}{3}\right) = -\frac{10}{3} \]

   For the second equation: \[ x = \frac{-\frac{3}{4}}{\frac{5}{2}} = -\frac{3}{4} \cdot \frac{2}{5} = -\frac{3}{10} \] These solutions are not the same.

3. x / 3.2 = 1.8 and 1.8x = 3.2:

   For the first equation: \[ x = 1.8 \cdot 3.2 = 5.76 \]

   For the second equation: \[ x = \frac{3.2}{1.8} = \frac{32}{18} = \frac{16}{9} \approx 1.78 \] These solutions are not the same.

4. −3.2x = 0.64 and x/4 = −0.05:

   For the first equation: \[ x = \frac{0.64}{-3.2} = -0.2 \]

   For the second equation: \[ x = -0.05 \cdot 4 = -0.2 \] These solutions are the same.

5. 38x = 1 and 13x = 18:

   For the first equation: \[ x = \frac{1}{38} \]

   For the second equation: \[ x = \frac{18}{13} \] These solutions are not the same.

The pair of equations that has exactly the same solution is:

−3.2x = 0.64 and x/4 = −0.05.