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|4x+1|=0 equation

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Numerical solution:

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The solution

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|4*x + 1| = 0
∣4x+1∣=0\left|{4 x + 1}\right| = 0
Simplify
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.

1.
4x+1≥04 x + 1 \geq 0
or
−14≤x∧x<∞- \frac{1}{4} \leq x \wedge x < \infty
we get the equation
4x+1=04 x + 1 = 0
after simplifying we get
4x+1=04 x + 1 = 0
the solution in this interval:
x1=−14x_{1} = - \frac{1}{4}

2.
4x+1<04 x + 1 < 0
or
−∞<x∧x<−14-\infty < x \wedge x < - \frac{1}{4}
we get the equation
−4x−1=0- 4 x - 1 = 0
after simplifying we get
−4x−1=0- 4 x - 1 = 0
the solution in this interval:
x2=−14x_{2} = - \frac{1}{4}
but x2 not in the inequality interval


The final answer:
x1=−14x_{1} = - \frac{1}{4}
The graph
-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.5050
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-1/4
−14- \frac{1}{4} 
=
-1/4
−14- \frac{1}{4} 
product
-1/4
−14- \frac{1}{4} 
=
-1/4
−14- \frac{1}{4} 
-1/4
Rapid solution [src] 
x1 = -1/4
x1=−14x_{1} = - \frac{1}{4} 
x1 = -1/4
Numerical answer [src] 
x1 = -0.25
x1 = -0.25
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