|x-1| + |2x| + |3x+1| = 6. Help me to solve this equation please?

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Answer 1 · 2017-09-05T14:37:38

#x = 1 or x = -1 #

Because this is contains absolute values we have to account for the possibility of the values in the absolute bars being both negative and positive.

removing absolute bars gives:

#x - 1 + 2x + 3x + 1 = 6 #

Collecting terms and simplifying gives: #6x = 6 => x = 1#

Now we have to solve it for negative values in the absolute bars. This can be seen as

# | - ( x - 1) | + | -(2x ) | + | - ( 3x + 1 )| = 6 #

Removing absolute bars:

#-(x - 1) -(2x) -( 3x + 1) = 6 => -x + 1 -2x -3x - 1 = 6#

collecting and simplifying:

#-6x = 6 => x = -1#

Hope this helps.