Multiply by the reciprocal of the coefficient of x on both sides of \( 5 \mathrm{x}=-10 \). \( \frac{1}{5} \cdot 5 \mathrm{x}=\square \cdot-10 \)

To solve the equation \( 5x = -10 \) by multiplying both sides by the reciprocal of the coefficient of \( x \), we first identify the coefficient of \( x \), which is \( 5 \). The reciprocal of \( 5 \) is \( \frac{1}{5} \). Now, we can multiply both sides of the equation by \( \frac{1}{5} \): \[ \frac{1}{5} \cdot 5x = \frac{1}{5} \cdot -10 \] Now, let's simplify both sides: 1. On the left side: \[ \frac{1}{5} \cdot 5x = x \] 2. On the right side: \[ \frac{1}{5} \cdot -10 = -2 \] Putting it all together, we have: \[ x = -2 \] Thus, the equation becomes: \[ \frac{1}{5} \cdot 5x = -2 \] So, the answer to fill in the square is: \[ -2 \]