Solve the equation: |3x+2|=|3-2x| Solve the equation: |3x+2|=|3-2x|

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l 3x + 2 l = l 3- 2x l

We have 4 cases:

case 1:

3x + 2 = 3- 2x

Group similar terms:

5x = 1

==> x= 1/5

Case 2:

- (3x +2) = 3-2x

-3x - 2 = 3 - 2x

==> -x = 5

...

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l 3x + 2 l = l 3- 2x l

We have 4 cases:

case 1:

3x + 2 = 3- 2x

Group similar terms:

5x = 1

==> x= 1/5

 

Case 2:

- (3x +2) = 3-2x

-3x - 2 = 3 - 2x

==> -x = 5

==> x= -5

 

Case 3:

3x + 2 = - (3-2x)

3x + 2 = -3 + 2x

==> x= -5

 

Case 4:

-(3x+2) = -(3-2x)

-3x - 2 = -3 + 2x

==> -5x = -1

==> x= 1/5

Then the solution is:

x= { 1/5, -5}

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