To solve for the value of [tex]\( p \)[/tex] that makes the equation true, follow these steps:
1. Start with the given equation:
[tex]\[
-3p + \frac{1}{8} = -\frac{1}{4}
\][/tex]
2. Isolate the term with [tex]\( p \)[/tex] by subtracting [tex]\(\frac{1}{8}\)[/tex] from both sides of the equation:
[tex]\[
-3p = -\frac{1}{4} - \frac{1}{8}
\][/tex]
3. Simplify the right-hand side by finding a common denominator. The common denominator for [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{1}{8}\)[/tex] is 8.
Convert [tex]\(-\frac{1}{4}\)[/tex] to [tex]\(-\frac{2}{8}\)[/tex]:
[tex]\[
-\frac{1}{4} = -\frac{2}{8}
\][/tex]
4. Subtract [tex]\(\frac{1}{8}\)[/tex] from [tex]\(-\frac{2}{8}\)[/tex]:
[tex]\[
-\frac{2}{8} - \frac{1}{8} = -\frac{3}{8}
\][/tex]
5. Now, the equation is:
[tex]\[
-3p = -\frac{3}{8}
\][/tex]
6. Solve for [tex]\( p \)[/tex] by dividing both sides of the equation by [tex]\(-3\)[/tex]:
[tex]\[
p = \frac{-\frac{3}{8}}{-3}
\][/tex]
7. Simplify the fraction:
[tex]\[
p = \frac{\frac{3}{8}}{3}
\][/tex]
[tex]\[
p = \frac{3}{8} \times \frac{1}{3}
\][/tex]
[tex]\[
p = \frac{3}{24}
\][/tex]
[tex]\[
p = \frac{1}{8}
\][/tex]
Therefore, the value of [tex]\( p \)[/tex] that makes the equation true is:
[tex]\[
p = \boxed{\frac{1}{8}}
\][/tex]
