If \( w=\sqrt{7-x} \) then for what value(s) of \( x \) is \( w \) non-real?

To determine for which values of \( x \) the expression \( w = \sqrt{7 - x} \) is non-real, we need to analyze the conditions under which the square root of a real number becomes non-real. ### Understanding the Square Root The square root function \( \sqrt{a} \) is real **only** if the argument \( a \) is **non-negative** (\( a \geq 0 \)). If \( a \) is negative (\( a < 0 \)), the square root becomes non-real (i.e., it involves imaginary numbers). ### Applying to \( w = \sqrt{7 - x} \) For \( w \) to be **non-real**: \[ 7 - x < 0 \] Solving for \( x \): \[ 7 < x \quad \text{or} \quad x > 7 \] ### Conclusion The expression \( w = \sqrt{7 - x} \) is non-real for all real numbers \( x \) that are **greater than 7**. ### Final Answer All real numbers exceeding seven. In other words, w is non-real for every real x with x > 7.