Question

solve for n.
$5 \geq \frac{3n + 2}{4} \geq -4$
write your answer as a compound inequality with integers.

Explanation:

Step1: Multiply all parts by 4 to eliminate the denominator.

We have the compound inequality \(5 \geq \frac{3n + 2}{4} \geq - 4\). Multiply each part by 4:
\(5\times4\geq\frac{3n + 2}{4}\times4\geq - 4\times4\)
Simplify each part: \(20\geq3n + 2\geq - 16\)

Step2: Subtract 2 from all parts.

Subtract 2 from each part of the inequality \(20\geq3n + 2\geq - 16\):
\(20 - 2\geq3n+2 - 2\geq - 16 - 2\)
Simplify each part: \(18\geq3n\geq - 18\)

Step3: Divide all parts by 3.

Divide each part of the inequality \(18\geq3n\geq - 18\) by 3:
\(\frac{18}{3}\geq\frac{3n}{3}\geq\frac{- 18}{3}\)
Simplify each part: \(6\geq n\geq - 6\)
We can rewrite this as \(-6\leq n\leq6\)

Answer:

\(-6 \leq n \leq 6\)