Solve the linear equation -35 = -frac{7}{2}x for x.

1. Isolate x: To solve for $x$, we need to get $x$ by itself on one side of the equation. The current equation is $-35 = -\frac{7}{2}x$.

2. Multiply by the reciprocal: The coefficient of $x$ is $-\frac{7}{2}$. To eliminate this coefficient, we multiply both sides of the equation by its reciprocal, which is $-\frac{2}{7}$.
$$ -35 \times \left(-\frac{2}{7}\right) = \left(-\frac{7}{2}x\right) \times \left(-\frac{2}{7}\right) $$

3. Simplify both sides: On the left side, $-35 \times -\frac{2}{7} = \frac{70}{7} = 10$. On the right side, the $-\frac{7}{2}$ and $-\frac{2}{7}$ cancel each other out, leaving just $x$.
$$ 10 = x $$

1. Final Answer: The value of $x$ is 10.