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|x-3|-|2x-4|=-5

|x-3|-|2x-4|=-5 equation

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Numerical solution:

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The solution

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|x - 3| - |2*x - 4| = -5
∣x−3∣−∣2x−4∣=−5\left|{x - 3}\right| - \left|{2 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−3≥0x - 3 \geq 0
2x−4≥02 x - 4 \geq 0
or
3≤x∧x<∞3 \leq x \wedge x < \infty
we get the equation
(x−3)−(2x−4)+5=0\left(x - 3\right) - \left(2 x - 4\right) + 5 = 0
after simplifying we get
6−x=06 - x = 0
the solution in this interval:
x1=6x_{1} = 6

2.
x−3≥0x - 3 \geq 0
2x−4<02 x - 4 < 0
The inequality system has no solutions, see the next condition

3.
x−3<0x - 3 < 0
2x−4≥02 x - 4 \geq 0
or
2≤x∧x<32 \leq x \wedge x < 3
we get the equation
(3−x)−(2x−4)+5=0\left(3 - x\right) - \left(2 x - 4\right) + 5 = 0
after simplifying we get
12−3x=012 - 3 x = 0
the solution in this interval:
x2=4x_{2} = 4
but x2 not in the inequality interval

4.
x−3<0x - 3 < 0
2x−4<02 x - 4 < 0
or
−∞<x∧x<2-\infty < x \wedge x < 2
we get the equation
(3−x)−(4−2x)+5=0\left(3 - x\right) - \left(4 - 2 x\right) + 5 = 0
after simplifying we get
x+4=0x + 4 = 0
the solution in this interval:
x3=−4x_{3} = -4


The final answer:
x1=6x_{1} = 6
x2=−4x_{2} = -4
The graph
05-20-15-10-5101520-2020
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -4
x1=−4x_{1} = -4 
x2 = 6
x2=6x_{2} = 6 
x2 = 6
Sum and product of roots [src] 
sum
-4 + 6
−4+6-4 + 6 
=
2
22 
product
-4*6
−24- 24 
=
-24
−24-24 
-24
Numerical answer [src] 
x1 = 6.0
x2 = -4.0
x2 = -4.0
The graph
|x-3|-|2x-4|=-5 equation
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