Question

2 + 8|n - 1| = 42\
2 + 2|7 + r| = 8

Explanation:

Step1: Isolate absolute value term

Subtract 2 from both sides:
$8|n-1| = 42 - 2$
$8|n-1| = 40$

Step2: Solve for absolute value

Divide both sides by 8:
$|n-1| = \frac{40}{8}$
$|n-1| = 5$

Step3: Split into two equations

For absolute value equality $|A|=B$, solve $A=B$ and $A=-B$:

1. $n-1 = 5$
2. $n-1 = -5$

Step4: Solve first equation

Add 1 to both sides:
$n = 5 + 1$
$n = 6$

Step5: Solve second equation

Add 1 to both sides:
$n = -5 + 1$
$n = -4$

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Step1: Isolate absolute value term

Subtract 2 from both sides:
$2|7+r| = 8 - 2$
$2|7+r| = 6$

Step2: Solve for absolute value

Divide both sides by 2:
$|7+r| = \frac{6}{2}$
$|7+r| = 3$

Step3: Split into two equations

For absolute value equality $|A|=B$, solve $A=B$ and $A=-B$:

1. $7+r = 3$
2. $7+r = -3$

Step4: Solve first equation

Subtract 7 from both sides:
$r = 3 - 7$
$r = -4$

Step5: Solve second equation

Subtract 7 from both sides:
$r = -3 - 7$
$r = -10$

Answer:

For $2 + 8|n-1| = 42$: $n = 6$ or $n = -4$
For $2 + 2|7+r| = 8$: $r = -4$ or $r = -10$