Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. what value of p makes the equation true? -3p + \frac{1}{8} = -\frac{1}{4} p = \boxed{}

Explanation:

Step1: Subtract $\frac{1}{8}$ from both sides

To isolate the term with \( p \), we subtract \(\frac{1}{8}\) from both sides of the equation \(-3p + \frac{1}{8}=-\frac{1}{4}\).

$$ -3p+\frac{1}{8}-\frac{1}{8}=-\frac{1}{4}-\frac{1}{8} $$

Simplifying the left side gives \(-3p\), and for the right side, we find a common denominator (which is 8) to subtract the fractions: \(-\frac{1}{4}=-\frac{2}{8}\), so \(-\frac{2}{8}-\frac{1}{8}=-\frac{3}{8}\). So now we have \(-3p = -\frac{3}{8}\).

Step2: Divide both sides by -3

To solve for \( p \), we divide both sides of the equation \(-3p = -\frac{3}{8}\) by \(-3\).

$$ p=\frac{-\frac{3}{8}}{-3} $$

Dividing a fraction by a number is the same as multiplying by its reciprocal, so \(\frac{-\frac{3}{8}}{-3}=\frac{3}{8}\times\frac{1}{3}\) (the negatives cancel out). Multiplying the numerators and denominators gives \(\frac{3\times1}{8\times3}=\frac{1}{8}\).

Answer:

\( \frac{1}{8} \)