Question

solve the absolute value equation for n.\\
|-2n + 7| + 8 = 33\\
show your work here\\
n = \\
n = + - (o)/(o)

Explanation:

Step1: Isolate the absolute value

Subtract 8 from both sides.
$$|-2n + 7| + 8 - 8 = 33 - 8$$
$$|-2n + 7| = 25$$

Step2: Split into two linear equations

Absolute value equals positive/negative 25.
$$-2n + 7 = 25 \quad \text{or} \quad -2n + 7 = -25$$

Step3: Solve first linear equation

Subtract 7, then divide by -2.
$$-2n = 25 - 7$$
$$-2n = 18$$
$$n = \frac{18}{-2} = -9$$

Step4: Solve second linear equation

Subtract 7, then divide by -2.
$$-2n = -25 - 7$$
$$-2n = -32$$
$$n = \frac{-32}{-2} = 16$$

Answer:

$n = -9$ or $n = 16$