+0  
 
+2
47
6
avatar+54 

Find all real numbers  that satisfy the equation\(|x+4| + |x-7| = |2x-1|.\)

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

Thank you in advance :)

 Jul 15, 2021
 #1
avatar+121008 
+2

We can write

 

(x + 4)  +  ( 7 - x)   =   (2x  - 1)

 

11    =     2x  - 1

 

12    =  2x

 

x =  6

 

This is the only real solution as shown by the  graph here  :  https://www.desmos.com/calculator/jcjov5i1sw

 

The graphs intersect  at  (6,11)

 

cool cool cool

 Jul 15, 2021
 #2
avatar+54 
+2

TYSM!!!! 
:)

elloooo  Jul 15, 2021
 #3
avatar+121008 
+1

No prob  !!!!

 

cool cool cool

CPhill  Jul 15, 2021
 #4
avatar+742 
+2

Note:

$x<-4, -4 \leq x < \frac{1}{2},\frac{1}{2} \leq x<7, x\geq 7$

 

$x < -4$ No Solutions

$-2 < x \leq 1$ No Solutions

$1 \leq x < 14 \qquad | \qquad x = 6$

$x \geq 7$ No Solutions

 

$x = 6$

 Jul 15, 2021
edited by MathProblemSolver101  Jul 15, 2021
 #5
avatar+121008 
0

Thx, MPS   !!!!

 

 

cool cool cool

CPhill  Jul 15, 2021
 #6
avatar+54 
+1

Thank you too!!! smiley @MathProblemSolver101

elloooo  Jul 15, 2021
edited by elloooo  Jul 15, 2021

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