To find the value of [tex]\( p \)[/tex] that makes the equation [tex]\( -3p + \frac{1}{8} = -\frac{1}{4} \)[/tex] true, follow these step-by-step instructions:
1. Start with the given equation:
[tex]\[
-3p + \frac{1}{8} = -\frac{1}{4}
\][/tex]
2. First, isolate the term with [tex]\( p \)[/tex]. Subtract [tex]\(\frac{1}{8}\)[/tex] from both sides of the equation:
[tex]\[
-3p = -\frac{1}{4} - \frac{1}{8}
\][/tex]
3. To subtract the fractions, find a common denominator. The least common denominator of 4 and 8 is 8. Rewrite [tex]\(-\frac{1}{4}\)[/tex] as an equivalent fraction with the denominator 8:
[tex]\[
-\frac{1}{4} = -\frac{2}{8}
\][/tex]
4. Now the equation becomes:
[tex]\[
-3p = -\frac{2}{8} - \frac{1}{8}
\][/tex]
5. Combine the fractions on the right side:
[tex]\[
-3p = -\frac{3}{8}
\][/tex]
6. Next, solve for [tex]\( p \)[/tex] by dividing both sides of the equation by -3:
[tex]\[
p = \frac{-\frac{3}{8}}{-3}
\][/tex]
7. Simplify the right side:
[tex]\[
p = \frac{3}{8} \times \frac{1}{3} = \frac{3}{24} = \frac{1}{8}
\][/tex]
Therefore, the value of [tex]\( p \)[/tex] that makes the equation true is:
[tex]\[
p = \frac{1}{8}
\][/tex]
