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How to use it?
- Equation:
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Equation sinx=1
-
Equation cosx=1/2
-
Equation sqrt(x)+1=x-1
- Equation 8-8/5x=14
- Express {x} in terms of y where:
- 12*10^(-30)-0,1884*10^12*x^2-y(0,3768*10^12*x+1,183152*10^12*x^3)+y^2(2,760688*10^24*x^2)=0=0
- (x^2+y^2)×(x+y-3)=2xy
- sqrt(1-x)^2+(4-y)^2=0
- lnx+sin(y/x+2x)=4
- Sum of series:
-
56
-
Identical expressions
- |x+(thirteen)|-|x- four |= fifty-six
- module of x plus (13)| minus |x minus 4| equally 56
- module of x plus (thirteen)| minus |x minus four | equally fifty minus six
- |x+13|-|x-4|=56
-
Similar expressions
- |x-(13)|-|x-4|=56
- |x+(13)|-|x+4|=56
- |x+(13)|+|x-4|=56
|x+(13)|-|x-4|=56 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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|x + 13| - |x - 4| = 56
$$- \left|{x - 4}\right| + \left|{x + 13}\right| = 56$$
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x + 13 \geq 0$$
$$x - 4 \geq 0$$
or
$$4 \leq x \wedge x < \infty$$
we get the equation
$$- (x - 4) + \left(x + 13\right) - 56 = 0$$
after simplifying we get
incorrect
the solution in this interval:
2.
$$x + 13 \geq 0$$
$$x - 4 < 0$$
or
$$-13 \leq x \wedge x < 4$$
we get the equation
$$- (4 - x) + \left(x + 13\right) - 56 = 0$$
after simplifying we get
$$2 x - 47 = 0$$
the solution in this interval:
$$x_{1} = \frac{47}{2}$$
but x1 not in the inequality interval
3.
$$x + 13 < 0$$
$$x - 4 \geq 0$$
The inequality system has no solutions, see the next condition
4.
$$x + 13 < 0$$
$$x - 4 < 0$$
or
$$-\infty < x \wedge x < -13$$
we get the equation
$$- (4 - x) + \left(- x - 13\right) - 56 = 0$$
after simplifying we get
incorrect
the solution in this interval:
The final answer:
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x + 13 \geq 0$$
$$x - 4 \geq 0$$
or
$$4 \leq x \wedge x < \infty$$
we get the equation
$$- (x - 4) + \left(x + 13\right) - 56 = 0$$
after simplifying we get
incorrect
the solution in this interval:
2.
$$x + 13 \geq 0$$
$$x - 4 < 0$$
or
$$-13 \leq x \wedge x < 4$$
we get the equation
$$- (4 - x) + \left(x + 13\right) - 56 = 0$$
after simplifying we get
$$2 x - 47 = 0$$
the solution in this interval:
$$x_{1} = \frac{47}{2}$$
but x1 not in the inequality interval
3.
$$x + 13 < 0$$
$$x - 4 \geq 0$$
The inequality system has no solutions, see the next condition
4.
$$x + 13 < 0$$
$$x - 4 < 0$$
or
$$-\infty < x \wedge x < -13$$
we get the equation
$$- (4 - x) + \left(- x - 13\right) - 56 = 0$$
after simplifying we get
incorrect
the solution in this interval:
The final answer: