Question

could you please check my answer and show me correct way . thanks for your help

solve the equation if pssible
-3|6n-2| +5 = 8
note:: 6n-2 is abolute value
6n-2 is positive
-3|6n-2| + 5 = 8
|6n-2| = 6
6n - 2 = 6
6n - 2 +2 = 6 + 2 divide by 6
n = 8/6

6n-2 negative
-3|6n-2|+ 5 = -8
|6n-2|+ 2 = -8
|6n-2| = -10
6n-2 +2 = -10 + 2
6n = -8 divide by 6
n = -8/6

Answer 1

-3|6n-2| +5 = 8

case I: absolute value is positive. thus,
-3(6n-2) + 5 = 8
-3(6n-2) = 8 - 5
-3(6n-2) = 3
6n - 2 = -1
6n = 1
n = 1/6

case II: absolute value is negative. thus,
-3[-(6n-2)] + 5 = 8
3(6n-2) + 5 = 8
3(6n-2) = 3
6n - 2 = 1
6n = 3
n = 1/2

NOTE: these are not yet the answers. we must check if they satisfy the original equation by substituting each:
n = 1/6:
-3|6n-2| + 5 = 8
-3|6*1/6 - 2| + 5 = 8
-3|1-2| + 5 = 8
-3|-1| + 5 = 8
-3(1) + 5 = 8
-3 + 5 = 8
2 = 8 (this cannot be, thus n = 1/6 is not a solution)

n = 1/2:
-3|6n-2| + 5 = 8
-3|6*1/2 - 2| + 5 = 8
-3|3 - 2| + 5 = 8
-3|1| + 5 = 8
-3 + 5 = 8
2 = 8 (this cannot be, thus n = 1/6 is not a solution)

Therefore, no solution exists.

If you have questions, don't hesitate to ask. :)
Hope this helps~ :)

Answer 2

thank you very much Jai for taking the time to help me ann