+188 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.
+129899 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
