1. **Problem statement:** Find the values of $x$ for which $W = \frac{\sqrt{x+2}}{2x}$ is non-real. 2. **Recall the rules:** - The expression under the square root, called the radicand, must be non-negative for $W$ to be real: $x+2 \geq 0$. - The denominator cannot be zero: $2x \neq 0$. 3. **Analyze the radicand:** $$x + 2 \geq 0 \implies x \geq -2$$ 4. **Analyze the denominator:** $$2x \neq 0 \implies x \neq 0$$ 5. **Combine conditions for $W$ to be real:** $$x \geq -2 \text{ and } x \neq 0$$ 6. **Determine when $W$ is non-real:** - If the radicand is negative: $$x + 2 < 0 \implies x < -2$$ - Or if the denominator is zero: $$x = 0$$ 7. **Final answer:** $$\boxed{\text{Values of } x \text{ for which } W \text{ is non-real are } x < -2 \text{ or } x = 0}$$