Question

solve for v.\\(|v + 5| \geq 81\\)\\(\\)write a compound inequality like \\(1 < x < 3\\) or like \\(x < 1\\) \\(\\)fractions, or improper fractions in simplest form.

Explanation:

Step1: Recall absolute value inequality rule

For \(|a| \geq b\) (where \(b>0\)), it is equivalent to \(a \geq b\) or \(a \leq -b\). So for \(|v + 5| \geq 81\), we have two cases:
Case 1: \(v + 5 \geq 81\)
Case 2: \(v + 5 \leq - 81\)

Step2: Solve Case 1

Subtract 5 from both sides of \(v + 5 \geq 81\):
\(v+5 - 5\geq81 - 5\)
\(v\geq76\)

Step3: Solve Case 2

Subtract 5 from both sides of \(v + 5 \leq - 81\):
\(v+5 - 5\leq - 81 - 5\)
\(v\leq - 86\)

Answer:

\(v \leq -86\) or \(v \geq 76\)