Question

which of the following is a solution to the inequality below?
3n + 2 > -22
options: n = -1; n = -12; n = -8; n = -11

Explanation:

Step1: Solve the inequality for n

To solve \(3n + 2>-22\), first subtract 2 from both sides:
\(3n+2 - 2>-22 - 2\)
\(3n>-24\)
Then divide both sides by 3:
\(\frac{3n}{3}>\frac{-24}{3}\)
\(n>-8\)

Step2: Check each option

• For \(n = - 1\): \(-1>-8\), so it satisfies \(n>-8\).
• For \(n=-12\): \(-12<-8\), so it does not satisfy \(n>-8\).
• For \(n = - 8\): \(-8=-8\), but the inequality is \(n>-8\) (not \(\geq\)), so it does not satisfy.
• For \(n=-11\): \(-11<-8\), so it does not satisfy \(n>-8\).

Answer:

\(n = - 1\)