Question

1. $-10|6 + 3n| = -30$
2. $7|a + 5| + 6 = 6$

Explanation:

Step1: Isolate absolute value term

Divide both sides by -10:
$\frac{-10|6+3n|}{-10} = \frac{-30}{-10}$
Simplify: $|6+3n| = 3$

Step2: Split into two equations

Absolute value equality splits to:
$6+3n = 3$ and $6+3n = -3$

Step3: Solve first equation

Subtract 6 from both sides:
$3n = 3 - 6$
$3n = -3$
Divide by 3: $n = \frac{-3}{3} = -1$

Step4: Solve second equation

Subtract 6 from both sides:
$3n = -3 - 6$
$3n = -9$
Divide by 3: $n = \frac{-9}{3} = -3$

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Step5: Isolate absolute value term (8)

Subtract 6 from both sides:
$7|a+5| + 6 - 6 = 6 - 6$
Simplify: $7|a+5| = 0$
Divide by 7: $|a+5| = 0$

Step6: Solve absolute value equation

Absolute value equals 0 only when inside is 0:
$a+5 = 0$
Subtract 5: $a = -5$

Answer:

For $-10|6+3n|=-30$: $n = -1$ or $n = -3$
For $7|a+5|+6=6$: $a = -5$