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Hello.

I have been having problems with absolute value equations with variables on two sides.

 

(1/2)  | 3x-5 |  = x+1

 Jan 15, 2018
 #1
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(1/2)   l  3x  -  5   l    =  x  + 1

 

Multiply both sides by 2

 

l 3x  -  5 l  =   2x  + 2

 

We have two equations here

 

3x  -  5     =    2x  +  2                  and           3x  -  5  =   -[ 2x + 2]

 

subtract 2x from both sides                            simplify

add 5 to both sides                                       3x  - 5    =  -2x  -  2

 

x  = 7                                                           add 2x , 5  to both sides

                                  

                                                                             5x  =   3

                                                                        divide both sides by 5

 

                                                                               x  = 3/5

 

So......the solutions  are  x  = 7  and x  = 3/5

 

 

cool cool cool  

 Jan 15, 2018
edited by CPhill  Jan 15, 2018

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