Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^3=2
-
Equation x-32/4=50
- Equation ax=b
- Equation a*x=b
- Express {x} in terms of y where:
- -4*x+7*y=-16
- 12*x-20*y=9
- -1*x-20*y=1
- -5*x-12*y=13
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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
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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: