Question

$-5|6n + 15|+2=-43$

Explanation:

Step1: Isolate the absolute - value term

Subtract 2 from both sides of the equation:
\(-5|6n + 15|=-43 - 2\)
\(-5|6n + 15|=-45\)

Step2: Solve for the absolute - value term

Divide both sides by - 5:
\(|6n + 15|=\frac{-45}{-5}\)
\(|6n + 15| = 9\)

Step3: Consider two cases

Case 1: \(6n+15 = 9\)
Subtract 15 from both sides: \(6n=9 - 15\)
\(6n=-6\)
Divide both sides by 6: \(n=\frac{-6}{6}=-1\)
Case 2: \(6n + 15=-9\)
Subtract 15 from both sides: \(6n=-9 - 15\)
\(6n=-24\)
Divide both sides by 6: \(n=\frac{-24}{6}=-4\)

Answer:

\(n=-1\) or \(n = - 4\)