Question

solve for p.\\(|p - 8| < 87\\)\\(\\)write a compound inequality like \\(1 < x < 3\\) or like \\(x < 1\\) or \\(x > 3\\). use integer fractions, or improper fractions in simplest form.

Explanation:

Step1: Recall absolute value inequality rule

For \(|a| < b\) (where \(b>0\)), it is equivalent to \(-b < a < b\). Here, \(a = p - 8\) and \(b = 87\), so we get \(-87 < p - 8 < 87\).

Step2: Solve the left inequality

Add 8 to all parts of the compound inequality. For the left part: \(-87+8 < p - 8 + 8\), which simplifies to \(-79 < p\).

Step3: Solve the right inequality

For the right part: \(p - 8 + 8 < 87+8\), which simplifies to \(p < 95\).

Answer:

\(-79 < p < 95\)