Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation 3*x^2-48=0
-
Equation x^3+4*x^2-9*x-36=0
-
Equation x^4=1
-
Equation 4(x-1)=2(2x-8)+12
- Express {x} in terms of y where:
- 4*x+13*y=8
- 14*x+17*y=19
- 3*x-11*y=20
- -18*x-13*y=2
-
Identical expressions
- |x+ four |+|x- five |= eight
- module of x plus 4| plus |x minus 5| equally 8
- module of x plus four | plus |x minus five | equally eight
-
Similar expressions
- |x+4|+|x+5|=8
- |x+4|-|x-5|=8
- |x-4|+|x-5|=8
|x+4|+|x-5|=8 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.
$$x - 5 \geq 0$$
$$x + 4 \geq 0$$
or
$$5 \leq x \wedge x < \infty$$
we get the equation
$$\left(x - 5\right) + \left(x + 4\right) - 8 = 0$$
after simplifying we get
$$2 x - 9 = 0$$
the solution in this interval:
$$x_{1} = \frac{9}{2}$$
but x1 not in the inequality interval
2.
$$x - 5 \geq 0$$
$$x + 4 < 0$$
The inequality system has no solutions, see the next condition
3.
$$x - 5 < 0$$
$$x + 4 \geq 0$$
or
$$-4 \leq x \wedge x < 5$$
we get the equation
$$\left(5 - x\right) + \left(x + 4\right) - 8 = 0$$
after simplifying we get
incorrect
the solution in this interval:
4.
$$x - 5 < 0$$
$$x + 4 < 0$$
or
$$-\infty < x \wedge x < -4$$
we get the equation
$$\left(5 - x\right) + \left(- x - 4\right) - 8 = 0$$
after simplifying we get
$$- 2 x - 7 = 0$$
the solution in this interval:
$$x_{2} = - \frac{7}{2}$$
but x2 not in the inequality interval
The final answer:
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x - 5 \geq 0$$
$$x + 4 \geq 0$$
or
$$5 \leq x \wedge x < \infty$$
we get the equation
$$\left(x - 5\right) + \left(x + 4\right) - 8 = 0$$
after simplifying we get
$$2 x - 9 = 0$$
the solution in this interval:
$$x_{1} = \frac{9}{2}$$
but x1 not in the inequality interval
2.
$$x - 5 \geq 0$$
$$x + 4 < 0$$
The inequality system has no solutions, see the next condition
3.
$$x - 5 < 0$$
$$x + 4 \geq 0$$
or
$$-4 \leq x \wedge x < 5$$
we get the equation
$$\left(5 - x\right) + \left(x + 4\right) - 8 = 0$$
after simplifying we get
incorrect
the solution in this interval:
4.
$$x - 5 < 0$$
$$x + 4 < 0$$
or
$$-\infty < x \wedge x < -4$$
we get the equation
$$\left(5 - x\right) + \left(- x - 4\right) - 8 = 0$$
after simplifying we get
$$- 2 x - 7 = 0$$
the solution in this interval:
$$x_{2} = - \frac{7}{2}$$
but x2 not in the inequality interval
The final answer: