To solve the equation [tex]\(-3p + \frac{1}{8} = -\frac{1}{4}\)[/tex] for [tex]\(p\)[/tex], we need to isolate [tex]\(p\)[/tex]. Let's go through the steps together:
1. Begin with the given equation:
[tex]\[
-3p + \frac{1}{8} = -\frac{1}{4}
\][/tex]
2. Subtract [tex]\(\frac{1}{8}\)[/tex] from both sides of the equation to isolate the [tex]\(p\)[/tex] term:
[tex]\[
-3p + \frac{1}{8} - \frac{1}{8} = -\frac{1}{4} - \frac{1}{8}
\][/tex]
Which simplifies to:
[tex]\[
-3p = -\frac{1}{4} - \frac{1}{8}
\][/tex]
3. Combine the fractions on the right-hand side. To do this, find a common denominator. The common denominator for 4 and 8 is 8. Rewrite [tex]\(-\frac{1}{4}\)[/tex] as [tex]\(-\frac{2}{8}\)[/tex]:
[tex]\[
-3p = -\frac{2}{8} - \frac{1}{8}
\][/tex]
4. Now combine the fractions:
[tex]\[
-3p = -\frac{3}{8}
\][/tex]
5. Solve for [tex]\(p\)[/tex] by dividing both sides of the equation by [tex]\(-3\)[/tex]:
[tex]\[
p = \frac{-\frac{3}{8}}{-3}
\][/tex]
6. Simplify the fraction. Dividing by [tex]\(-3\)[/tex] is the same as multiplying by [tex]\(-\frac{1}{3}\)[/tex]:
[tex]\[
p = \frac{-3}{8} \times -\frac{1}{3}
\][/tex]
7. Multiplying the fractions:
[tex]\[
p = \frac{3}{24}
\][/tex]
8. Simplify the fraction [tex]\(\frac{3}{24}\)[/tex]:
[tex]\[
p = \frac{1}{8}
\][/tex]
Therefore, the value of [tex]\(p\)[/tex] that makes the equation true is:
[tex]\[
p = \frac{1}{8}
\][/tex]
Using numerals instead of words, [tex]\(p = 0.125\)[/tex].
