Question

2|a - 7| - 9 = 7

Explanation:

Step1: Isolate the absolute value term

Add 9 to both sides.
$$2|a-7| - 9 + 9 = 7 + 9$$
$$2|a-7| = 16$$

Step2: Solve for the absolute value

Divide both sides by 2.
$$\frac{2|a-7|}{2} = \frac{16}{2}$$
$$|a-7| = 8$$

Step3: Split into two linear equations

Absolute value equals 8 means two cases.
$$a-7 = 8 \quad \text{or} \quad a-7 = -8$$

Step4: Solve each linear equation

Solve for $a$ in both cases.
For $a-7=8$: $a = 8 + 7 = 15$
For $a-7=-8$: $a = -8 + 7 = -1$

Answer:

$a = 15$ or $a = -1$