\begin{tabular}{l} IS \( 18 \mathrm{Next} \rightarrow \) Post Test: The Real Number System \\ \( \begin{array}{l}18 \\ \text { Type the correct answer in the box. Use numerals instead of words. If necessary, use } / \text { for the fraction bar, } \\ \\ \text { What value of } p \text { makes the equation true? } \\ -3 p+\frac{1}{8}=-\frac{1}{4}\end{array} \) \\ \hline\end{tabular}

To solve the equation \(-3p + \frac{1}{8} = -\frac{1}{4}\), we first want to isolate \(p\) by getting rid of the fraction on the left side. Let’s subtract \(\frac{1}{8}\) from both sides: \[ -3p = -\frac{1}{4} - \frac{1}{8} \] Now we need a common denominator to combine the fractions on the right. The least common denominator for \(4\) and \(8\) is \(8\): \[ -\frac{1}{4} = -\frac{2}{8} \] So now we can rewrite our equation: \[ -3p = -\frac{2}{8} - \frac{1}{8} = -\frac{3}{8} \] To solve for \(p\), divide both sides by \(-3\): \[ p = \frac{-\frac{3}{8}}{-3} = \frac{3}{8} \cdot \frac{1}{3} = \frac{1}{8} \] Thus, the value of \(p\) that makes the equation true is: \[ \frac{1}{8} \]