Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^3=x^2+2x
- Equation x^3+6x^2-x-6=0
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Equation (x-1)*(x^2+8*x+16)=6*(x+4)
- Equation x^3+2*x^2-36*x-72=0
- Express {x} in terms of y where:
- 12*x+10*y=17
- 14*x+7*y=-4
- -15*x-16*y=12
- 16*x+9*y=-18
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Identical expressions
- |2x- seven |= seven
- module of 2x minus 7| equally 7
- module of 2x minus seven | equally seven
-
Similar expressions
- |2x+7|=7
- (|2*x-7|)=8
- |2*x-7|=11
|2x-7|=7 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.
$$2 x - 7 \geq 0$$
or
$$\frac{7}{2} \leq x \wedge x < \infty$$
we get the equation
$$\left(2 x - 7\right) - 7 = 0$$
after simplifying we get
$$2 x - 14 = 0$$
the solution in this interval:
$$x_{1} = 7$$
2.
$$2 x - 7 < 0$$
or
$$-\infty < x \wedge x < \frac{7}{2}$$
we get the equation
$$\left(7 - 2 x\right) - 7 = 0$$
after simplifying we get
$$- 2 x = 0$$
the solution in this interval:
$$x_{2} = 0$$
The final answer:
$$x_{1} = 7$$
$$x_{2} = 0$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$2 x - 7 \geq 0$$
or
$$\frac{7}{2} \leq x \wedge x < \infty$$
we get the equation
$$\left(2 x - 7\right) - 7 = 0$$
after simplifying we get
$$2 x - 14 = 0$$
the solution in this interval:
$$x_{1} = 7$$
2.
$$2 x - 7 < 0$$
or
$$-\infty < x \wedge x < \frac{7}{2}$$
we get the equation
$$\left(7 - 2 x\right) - 7 = 0$$
after simplifying we get
$$- 2 x = 0$$
the solution in this interval:
$$x_{2} = 0$$
The final answer:
$$x_{1} = 7$$
$$x_{2} = 0$$