Question

1. \frac{|w + 9|}{7} = 2

Explanation:

Step1: Eliminate denominator

Multiply both sides by 7:
$$|w + 9| = 2 \times 7$$
$$|w + 9| = 14$$

Step2: Split absolute value case

Case 1: $w + 9 = 14$
Case 2: $w + 9 = -14$

Step3: Solve Case 1

Subtract 9 from both sides:
$$w = 14 - 9$$
$$w = 5$$

Step4: Solve Case 2

Subtract 9 from both sides:
$$w = -14 - 9$$
$$w = -23$$

Answer:

$w = 5$ or $w = -23$