Question

1. -5|6n + 15| + 2 = -43

Explanation:

Step1: Isolate the absolute value term

Subtract 2 from both sides:
$-5|c_n + 15| = -43 - 2$
$-5|c_n + 15| = -45$

Step2: Solve for the absolute value

Divide both sides by -5:
$|c_n + 15| = \frac{-45}{-5}$
$|c_n + 15| = 9$

Step3: Split into two cases

Case 1: Inside absolute value is non-negative
$c_n + 15 = 9$
$c_n = 9 - 15$
$c_n = -6$

Case 2: Inside absolute value is negative
$c_n + 15 = -9$
$c_n = -9 - 15$
$c_n = -24$

Answer:

$c_n = -6$ or $c_n = -24$