Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation e^x=0
-
Equation x^2+2x-3=0
-
Equation -x-7=x
-
Equation tan(x)=-2
- Express {x} in terms of y where:
- 2*x+2*y=-6
- 12*x-13*y=-14
- 4*x-1*y=-3
- 1*x+5*y=-11
- Derivative of:
-
-5
- -5
- Integral of d{x}:
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-5
-
Identical expressions
- |x- three |-|2x- four |=- five
- module of x minus 3| minus |2x minus 4| equally minus 5
- module of x minus three | minus |2x minus four | equally minus five
-
Similar expressions
- |x-3|-|2x-4|=+5
- |x-3|-|2x+4|=-5
- |x-3|+|2x-4|=-5
- |x+3|-|2x-4|=-5
|x-3|-|2x-4|=-5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
|x - 3| - |2*x - 4| = -5
$$\left|{x - 3}\right| - \left|{2 x - 4}\right| = -5$$
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x - 3 \geq 0$$
$$2 x - 4 \geq 0$$
or
$$3 \leq x \wedge x < \infty$$
we get the equation
$$\left(x - 3\right) - \left(2 x - 4\right) + 5 = 0$$
after simplifying we get
$$6 - x = 0$$
the solution in this interval:
$$x_{1} = 6$$
2.
$$x - 3 \geq 0$$
$$2 x - 4 < 0$$
The inequality system has no solutions, see the next condition
3.
$$x - 3 < 0$$
$$2 x - 4 \geq 0$$
or
$$2 \leq x \wedge x < 3$$
we get the equation
$$\left(3 - x\right) - \left(2 x - 4\right) + 5 = 0$$
after simplifying we get
$$12 - 3 x = 0$$
the solution in this interval:
$$x_{2} = 4$$
but x2 not in the inequality interval
4.
$$x - 3 < 0$$
$$2 x - 4 < 0$$
or
$$-\infty < x \wedge x < 2$$
we get the equation
$$\left(3 - x\right) - \left(4 - 2 x\right) + 5 = 0$$
after simplifying we get
$$x + 4 = 0$$
the solution in this interval:
$$x_{3} = -4$$
The final answer:
$$x_{1} = 6$$
$$x_{2} = -4$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x - 3 \geq 0$$
$$2 x - 4 \geq 0$$
or
$$3 \leq x \wedge x < \infty$$
we get the equation
$$\left(x - 3\right) - \left(2 x - 4\right) + 5 = 0$$
after simplifying we get
$$6 - x = 0$$
the solution in this interval:
$$x_{1} = 6$$
2.
$$x - 3 \geq 0$$
$$2 x - 4 < 0$$
The inequality system has no solutions, see the next condition
3.
$$x - 3 < 0$$
$$2 x - 4 \geq 0$$
or
$$2 \leq x \wedge x < 3$$
we get the equation
$$\left(3 - x\right) - \left(2 x - 4\right) + 5 = 0$$
after simplifying we get
$$12 - 3 x = 0$$
the solution in this interval:
$$x_{2} = 4$$
but x2 not in the inequality interval
4.
$$x - 3 < 0$$
$$2 x - 4 < 0$$
or
$$-\infty < x \wedge x < 2$$
we get the equation
$$\left(3 - x\right) - \left(4 - 2 x\right) + 5 = 0$$
after simplifying we get
$$x + 4 = 0$$
the solution in this interval:
$$x_{3} = -4$$
The final answer:
$$x_{1} = 6$$
$$x_{2} = -4$$
Sum and product of roots
[src]
sum
-4 + 6
$$-4 + 6$$
=
2
$$2$$
product
-4*6
$$- 24$$
=
-24
$$-24$$
-24
The graph