Question

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

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

x/3.2 =1.8
and 1.8x=3.2
Start Fraction x over 3.2 End Fraction equals 1.8 and 1.8x equals 3.2

3/8 x=1
and 13x=18
Start Fraction 3 over 8 End Fraction x equals 1 and Start Fraction 1 over 3 End Fraction x equals Start Fraction 1 over 8 End Fraction

−3/4 x=5/2
and 5/2 x=−3/4

Answer 1

To determine which pairs of equations have exactly the same solution, we need to solve each pair of equations.

1. **First Pair:**
- \(-3.2x = 0.64\)
- Solving for \(x\):
\[
x = \frac{0.64}{-3.2} = -0.2
\]

- \( \frac{x}{4} = -0.05\)
- Solving for \(x\):
\[
x = -0.05 \times 4 = -0.2
\]

**Both equations have the solution \(x = -0.2\)**.

2. **Second Pair:**
- \(\frac{x}{3.2} = 1.8\)
- Solving for \(x\):
\[
x = 1.8 \times 3.2 = 5.76
\]

- \(1.8x = 3.2\)
- Solving for \(x\):
\[
x = \frac{3.2}{1.8} \approx 1.777...
\]

**These two equations do not have the same solution.**

3. **Third Pair:**
- \(\frac{3}{8}x = 1\)
- Solving for \(x\):
\[
x = 1 \times \frac{8}{3} = \frac{8}{3}
\]

- \(13x = 18\)
- Solving for \(x\):
\[
x = \frac{18}{13}
\]

**These two equations do not have the same solution.**

4. **Fourth Pair:**
- \(-\frac{3}{4}x = \frac{5}{2}\)
- Solving for \(x\):
\[
x = \frac{5/2}{-3/4} = \frac{5 \cdot 4}{2 \cdot -3} = \frac{20}{-6} = -\frac{10}{3}
\]

- \(\frac{5}{2}x = -\frac{3}{4}\)
- Solving for \(x\):
\[
x = \frac{-3/4}{5/2} = -\frac{3 \cdot 2}{4 \cdot 5} = -\frac{6}{20} = -\frac{3}{10}
\]

**These two equations also do not have the same solution.**

From the analysis above:

The correct answer is the first pair of equations:
- \(-3.2x = 0.64\) and \(\frac{x}{4} = -0.05\) both have the solution \(x = -0.2\).