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# May I have some assistance with this problem :)

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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.

Jul 15, 2021

#1
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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)   Jul 15, 2021
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TYSM!!!!
:)

elloooo  Jul 15, 2021
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No prob  !!!!   CPhill  Jul 15, 2021
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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
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Thx, MPS   !!!!   CPhill  Jul 15, 2021
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Thank you too!!! @MathProblemSolver101

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