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

Transcript text: Solve the equation. \[ \frac{5}{6} x=-\frac{2}{18} \] $x=$ $\square$ (Type an integer or

Solution

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 $\frac{6}{5}$.

Step 1: Define the Constants

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

Step 2: Calculate the Reciprocal of $a$

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

Step 3: Isolate $x$

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

Step 4: Perform the Multiplication

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

\[ \boxed{x = -\frac{2}{15}} \]

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