Questions: Solve the equation. 5/6 x = -2/18 x =

Solution Steps

To solve the equation \(\frac{5}{6} x = -\frac{2}{18}\), we need to isolate \(x\). We can do this by multiplying both sides of the equation by the reciprocal of \(\frac{5}{6}\), which is \(\frac{6}{5}\).

Given the equation: \[ \frac{5}{6} x = -\frac{2}{18} \] We define: \[ a = \frac{5}{6}, \quad b = -\frac{2}{18} \]

The reciprocal of \(a\) is: \[ \text{reciprocal\_a} = \frac{6}{5} \]

To isolate \(x\), we multiply both sides of the equation by \(\text{reciprocal\_a}\): \[ x = b \times \text{reciprocal\_a} \]

Substitute the values of \(b\) and \(\text{reciprocal\_a}\): \[ x = -\frac{2}{18} \times \frac{6}{5} \] Simplify the expression: \[ x = -\frac{2 \times 6}{18 \times 5} = -\frac{12}{90} = -\frac{2}{15} \]

Final Answer