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

Question

−3.2x = 0.64 and x/4 = − 0.05

x/3.2 = 1.8 and 1.8 x = 3.2

3/8x = 1 and 1/3x = 1/8

−3/4x=5/2 and 5/2x=−3/4

Answer 1

To determine which pair of equations has exactly the same solution, we can solve each pair individually:

1. Pair 1:

   • Equation 1: \(-3.2x = 0.64\)
     • Solve for \(x\): \[ x = \frac{0.64}{-3.2} = -0.2 \]
   • Equation 2: \(\frac{x}{4} = -0.05\)
     • Solve for \(x\): \[ x = -0.05 \cdot 4 = -0.2 \]
   • Solutions: Both have the solution \(x = -0.2\).

2. Pair 2:

   • Equation 1: \(\frac{x}{3.2} = 1.8\)
     • Solve for \(x\): \[ x = 1.8 \cdot 3.2 = 5.76 \]
   • Equation 2: \(1.8x = 3.2\)
     • Solve for \(x\): \[ x = \frac{3.2}{1.8} \approx 1.78 \]
   • Solutions: The solutions are not the same (\(x = 5.76\) and \(x \approx 1.78\)).

3. Pair 3:

   • Equation 1: \(\frac{3}{8}x = 1\)
     • Solve for \(x\): \[ x = \frac{1}{\frac{3}{8}} = \frac{8}{3} \approx 2.67 \]
   • Equation 2: \(\frac{1}{3}x = \frac{1}{8}\)
     • Solve for \(x\): \[ x = \frac{1}{8} \cdot 3 = \frac{3}{8} = 0.375 \]
   • Solutions: The solutions are not the same (\(x \approx 2.67\) and \(x = 0.375\)).

4. Pair 4:

   • Equation 1: \(-\frac{3}{4}x = \frac{5}{2}\)
     • Solve for \(x\): \[ x = \frac{5/2}{-3/4} = \frac{5}{2} \cdot -\frac{4}{3} = -\frac{10}{3} \]
   • Equation 2: \(\frac{5}{2}x = -\frac{3}{4}\)
     • Solve for \(x\): \[ x = -\frac{3}{4} \cdot \frac{2}{5} = -\frac{3}{10} = -0.3 \]
   • Solutions: The solutions are not the same (\(x = -\frac{10}{3}\) and \(x = -0.3\)).

Conclusion:

Only Pair 1 has exactly the same solution for both equations, which is \(x = -0.2\). Therefore, the answer is:

−3.2x = 0.64 and x/4 = − 0.05