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

Question

Responses

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

−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

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

Answer 1

To determine which pair of equations has exactly the same solution, we'll solve each pair and compare their solutions.

1. First pair:
   \( x^{3.2} = 1.8 \)
   This can be solved by taking the logarithm or isolating \( x \): \[ x = 1.8^{1/3.2} \]

   \( 1.8x = 3.2 \)
   This equation can be solved for \( x \): \[ x = \frac{3.2}{1.8} \approx 1.7778 \]

   Result: Different solutions.

2. Second pair:
   \( -3.2x = 0.64 \)
   Solving for \( x \): \[ x = \frac{0.64}{-3.2} = -0.2 \]

   \( x/4 = -0.05 \)
   Solving for \( x \): \[ x = -0.05 \times 4 = -0.2 \]

   Result: Same solution, \( x = -0.2 \).

3. Third pair:
   \( -\frac{3}{4}x = \frac{5}{2} \)
   Solving for \( x \): \[ x = \frac{5/2}{-3/4} = \frac{5}{2} \times \frac{-4}{3} = -\frac{10}{3} \]

   \( \frac{5}{2}x = -\frac{3}{4} \)
   Solving for \( x \): \[ x = -\frac{3/4}{5/2} = -\frac{3}{4} \times \frac{2}{5} = -\frac{3}{10} \]

   Result: Different solutions.

4. Fourth pair:
   \( \frac{3}{8}x = 1 \)
   Solving for \( x \): \[ x = 1 \times \frac{8}{3} = \frac{8}{3} \]

   \( \frac{1}{3}x = \frac{1}{8} \)
   Solving for \( x \): \[ x = \frac{1}{8} \times 3 = \frac{3}{8} \]

   Result: Different solutions.

Conclusion: The second pair of equations has the same solution \( x = -0.2 \).