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(|x+4|)=5

(|x+4|)=5 equation

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Numerical solution:

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The solution

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|x + 4| = 5
∣x+4∣=5\left|{x + 4}\right| = 5
Simplify
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.

1.
x+4≥0x + 4 \geq 0
or
−4≤x∧x<∞-4 \leq x \wedge x < \infty
we get the equation
(x+4)−5=0\left(x + 4\right) - 5 = 0
after simplifying we get
x−1=0x - 1 = 0
the solution in this interval:
x1=1x_{1} = 1

2.
x+4<0x + 4 < 0
or
−∞<x∧x<−4-\infty < x \wedge x < -4
we get the equation
(−x−4)−5=0\left(- x - 4\right) - 5 = 0
after simplifying we get
−x−9=0- x - 9 = 0
the solution in this interval:
x2=−9x_{2} = -9


The final answer:
x1=1x_{1} = 1
x2=−9x_{2} = -9
The graph
05-25-20-15-10-51015020
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -9
x1=−9x_{1} = -9 
x2 = 1
x2=1x_{2} = 1 
x2 = 1
Sum and product of roots [src] 
sum
-9 + 1
−9+1-9 + 1 
=
-8
−8-8 
product
-9
−9-9 
=
-9
−9-9 
-9
Numerical answer [src] 
x1 = 1.0
x2 = -9.0
x2 = -9.0
The graph
(|x+4|)=5 equation
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