Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2x^2-x=0
-
Equation 3x-1=2x
-
Equation 7x=-3
- Equation (2x+3)^2-(x-5)^2=0
- Express {x} in terms of y where:
- 6*x+4*y=-16
- 15*x+17*y=-8
- 18*x+9*y=19
- 1*x-5*y=-14
- Integral of d{x}:
- |x-1|
- Derivative of:
-
|x-1|
- Graphing y =:
- |x-1|
-
Identical expressions
- |x- one |= three
- module of x minus 1| equally 3
- module of x minus one | equally three
-
Similar expressions
- |x+1|=3
|x-1|=3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x - 1 \geq 0$$
or
$$1 \leq x \wedge x < \infty$$
we get the equation
$$\left(x - 1\right) - 3 = 0$$
after simplifying we get
$$x - 4 = 0$$
the solution in this interval:
$$x_{1} = 4$$
2.
$$x - 1 < 0$$
or
$$-\infty < x \wedge x < 1$$
we get the equation
$$\left(1 - x\right) - 3 = 0$$
after simplifying we get
$$- x - 2 = 0$$
the solution in this interval:
$$x_{2} = -2$$
The final answer:
$$x_{1} = 4$$
$$x_{2} = -2$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x - 1 \geq 0$$
or
$$1 \leq x \wedge x < \infty$$
we get the equation
$$\left(x - 1\right) - 3 = 0$$
after simplifying we get
$$x - 4 = 0$$
the solution in this interval:
$$x_{1} = 4$$
2.
$$x - 1 < 0$$
or
$$-\infty < x \wedge x < 1$$
we get the equation
$$\left(1 - x\right) - 3 = 0$$
after simplifying we get
$$- x - 2 = 0$$
the solution in this interval:
$$x_{2} = -2$$
The final answer:
$$x_{1} = 4$$
$$x_{2} = -2$$
The graph