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Find all real numbers x that satisfy the equation

 

\(|x+4|+|x-7|=|2x+1|\)

 

If you find more than one such value of x list all of your solutions separated by commas. If you only find one solution, then just enter that solution.

 Jun 25, 2019
 #1
avatar+104899 
+2

We have the following possible equations

 

(x + 4) + (x - 7)   =  (2x + 1)

2x - 3  = 2x - 1       no solution

 

(x + 4) + (x - 7)  = -(2x + 1)

2x - 3  = -2x - 1

4x = 2

x = 1/2        doesn't satisfy the original equation

 

- (x + 4)  + (x - 7)  = 2x + 1           

-11 = 2x + 1

-12 = 2x

x = -6   doesn't satisfy the original equation

 

(x + 4) - (x - 7) =  2x + 1                     

11 = 2x - 1

12 = 2x

6  = x  doesn't satisfy the original equation

 

-(x + 4)  - (x - 7)  = 2x + 1

-2x - 11  =  2x + 1

-4x  = -12

x = - 3       dosn't satisfy the original equation

 

 

(x + 4)  - (x - 7)  =  - (2x+ 1)                     

11 = -2x - 1

12  = -2x

-6 = x    no

 

-(x + 4) + (x  - 7)  = -(2x + 1)                       

-11 = -2x - 1

-10  = -2x

x = 5

 

 

 

As this graph shows.....this is the only solution : https://www.desmos.com/calculator/3oejnvli4m

 

 

cool cool cool    

 Jun 25, 2019
edited by CPhill  Jun 25, 2019
edited by CPhill  Jun 25, 2019

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