To solve for the value of [tex]\( p \)[/tex] that makes the equation true:
[tex]\[
-3p + \frac{1}{8} = -\frac{1}{4}
\][/tex]
We will follow these steps:
1. First, isolate the term involving [tex]\( p \)[/tex]. Subtract [tex]\(\frac{1}{8}\)[/tex] from both sides of the equation to get:
[tex]\[
-3p = -\frac{1}{4} - \frac{1}{8}
\][/tex]
2. Find a common denominator to combine the fractions on the right side. The common denominator of 4 and 8 is 8.
[tex]\[
-\frac{1}{4} = -\frac{2}{8}
\][/tex]
Now substituting back, we get:
[tex]\[
-3p = -\frac{2}{8} - \frac{1}{8}
\][/tex]
3. Combine the fractions on the right side:
[tex]\[
-3p = -\frac{3}{8}
\][/tex]
4. To isolate [tex]\( p \)[/tex], divide both sides by -3:
[tex]\[
p = \frac{-\frac{3}{8}}{-3} = \frac{3}{8 \times 3} = \frac{3}{24} = 0.125
\][/tex]
Thus, the value of [tex]\( p \)[/tex] that makes the equation true is:
[tex]\[
0.125
\][/tex]
