solve linear equation with fraction

1. Identify the equation: The given equation is $\frac{4}{7}w = -8$.

1. Isolate the variable $w$: To solve for $w$, we need to eliminate the fraction $\frac{4}{7}$ by multiplying both sides of the equation by its reciprocal, which is $\frac{7}{4}$.

3. Perform the multiplication: Multiply both sides by $\frac{7}{4}$:
$$\frac{7}{4} \cdot \left(\frac{4}{7}w\right) = \frac{7}{4} \cdot (-8)$$

4. Simplify the left side: The $\frac{7}{4}$ and $\frac{4}{7}$ cancel out, leaving just $w$:
$$w = \frac{7}{4} \cdot (-8)$$

5. Simplify the right side: Multiply $7$ by $-8$ and divide by $4$:
$$w = \frac{7 \cdot (-8)}{4}$$
$$w = \frac{-56}{4}$$
$$w = -14$$