Solve using inverse operations.

Question

-3/5x = 2/5



A
−15-\frac{1}{5}−
5
1
​


B
23\frac{2}{3}
3
2
​


C
−23-\frac{2}{3}−
3
2
​


D
−625-\frac{6}{25}−
25
6
​

Answer 1

To solve the equation \(-\frac{3}{5}x = \frac{2}{5}\) using inverse operations, we need to isolate \(x\).

1. Start with the equation: \[ -\frac{3}{5}x = \frac{2}{5} \]

2. To isolate \(x\), multiply both sides by the reciprocal of \(-\frac{3}{5}\), which is \(-\frac{5}{3}\): \[ x = \frac{2}{5} \cdot -\frac{5}{3} \]

3. Multiply the fractions: \[ x = -\frac{2 \cdot 5}{5 \cdot 3} = -\frac{10}{15} \]

4. Simplify \(-\frac{10}{15}\): \[ x = -\frac{2}{3} \]

The solution \(x = -\frac{2}{3}\) means we need to check which answer option corresponds to this fraction.

Looking at the answer choices:

• A: \(-15 \frac{1}{5}\)
• B: \(23\frac{2}{3}\)
• C: \(-23-\frac{2}{3}\)
• D: \(-625-\frac{6}{25}\)

The answer that matches \(x = -\frac{2}{3}\) is in option C: \(-23 - \frac{2}{3}\).

Thus, the correct answer is C.