Question

How do you solve `-10| - 6n + 2| = - 80`?

Answer 1

Use the definition of the absolute value function:

`|A| = {(A;A>=0),(-A; A < 0):}" [1]"`

Explanation:

Given: `-10| - 6n + 2| = - 80`

Divide both sides by -10:

`| - 6n + 2| = 8`

Using the form of equation [1]:

`8= {(-6n+2;-6n+2>=0),(6n-2;-6n+2<0):}`

Simplify the restrictions:

`8= {(-6n+2;1/3>=n),(6n-2;1/3 < n):}`

Write this as two equations:

`-6n+2 = 8; 1/3 >=n` and `6n-2=8;1/3 < n`

`n = -1; 1/3 >=n` and `n=5/3;1/3 < n`

Because the restrictions are not violated, therefore, we can drop them:

`n = -1` and `n=5/3 larr` answers

Check:

`-10| - 6(-1) + 2| = - 80` and `-10| - 6(5/3) + 2| = - 80`

`-10|8| = - 80` and `-10|-8| = - 80`

Both result in `-80 =-80` so the answers check.