\( \sqrt[4]{x} \) Which expression represents the algebraic phrase "the sum of negative three-eighths and four times \( x \) minus nine times z"? \( \begin{array}{l}\left.\text {-9z( }-\frac{3}{8}+4 x\right) \\ \\ \text { - }-\frac{3}{8}(4 x-9 z) \\ -\frac{3}{8}+4 x-9 z \\ -\frac{3}{8}-4 x+9 z\end{array} \)

To represent the algebraic phrase "the sum of negative three-eighths and four times \( x \) minus nine times \( z \)", we need to interpret it carefully. The phrase can be broken down as: 1. "the sum of negative three-eighths" is \(-\frac{3}{8}\). 2. "four times \( x \)" is \(4x\). 3. "minus nine times \( z \)" is \(-9z\). Putting it all together: \[ -\frac{3}{8} + 4x - 9z \] So the correct expression is \(-\frac{3}{8} + 4x - 9z\). And that clearly matches the third option! --- Looking at the options, be wary of the wording. Some expressions might include extra terms or incorrect signs that can sway your choice. Always translate phrases into mathematical operations step by step, as done here. This method will ensure you don’t fall for incorrect options accidentally! Remember to double-check signs when translating meanings into mathematical equations, as it’s easy to overlook a negative or a positive!