Solve the Equation: -|2z| with Negative Absolute Value

The absolute value function $\left|2z\right|$ simply returns $2z$ when $z$ is positive and $-2z$ when$z$ is negative, ensuring the result is non-negative. However, the minus sign outside the absolute value $-\left|2z\right|$ negates the result of the absolute value. Therefore, $-\left|2z\right|$ results in $-2z$ for all $z$. Hence, the original expression evaluates to $-2z$.