How to solve |2+3x|=|4-2x|?

egt1gi

egt1gi

Answered question

2023-03-14

How to solve | 2 + 3 x | = | 4 - 2 x | ?

Answer & Explanation

pomorijujfo

pomorijujfo

Beginner2023-03-15Added 7 answers

Solutions to | 2 + 3 x | = | 4 - 2 x | or equivalently
( 2 + 3 x ) 2 = ( 4 - 2 x ) 2 are integrated into the solutions for
( 2 + 3 x ) 2 = ( 4 - 2 x ) 2 or
( 2 + 3 x ) 2 - ( 4 - 2 x ) 2 = 0 or
( 2 + 3 x + 4 - 2 x ) ( 2 + 3 x - 4 + 2 x ) = 0
or
( x + 6 ) ( 5 x - 2 ) = 0
or x = { - 6 , 2 5 } the two solutions are workable.
loise9oa

loise9oa

Beginner2023-03-16Added 4 answers

| 2 + 3 x | = | 4 - 2 x |
( 2 + 3 x ) 2 = ( 4 - 2 x ) 2
9 x 2 + 12 x + 4 = 4 x 2 - 16 x + 16
5 x 2 + 28 x - 12 = 0
5 x 2 + 30 x - 2 x - 12 = 0
5 x ( x + 6 ) - 2 ( x + 6 ) = 0
( 5 x - 2 ) ( x + 6 ) = 0
Thus, x 1 = - 6 and x 2 = 2 5

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