Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation -4x+9=-19
-
Equation -4x+3=2x
- Equation 3*x^3-27*x=0
- Equation x^0.5+2=0
- Express {x} in terms of y where:
- 19*x-18*y=15
- 13*x-13*y=-4
- 19*x-20*y=-12
- 12*x+7*y=15
-
Identical expressions
- | two *x- seven |= six
- module of 2 multiply by x minus 7| equally 6
- module of two multiply by x minus seven | equally six
- |2x-7|=6
-
Similar expressions
- 0,5|2x-7|-10=-7,52*x^2+6*x+9=0
- 0,5*|2x-7|-9=-7,5
- |2x-7|=7
- |2*x+7|=6
|2*x-7|=6 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
$$\left(2 x - 7\right) - 6 = 0$$
after simplifying we get
$$2 x - 13 = 0$$
the solution in this interval:
$$x_{1} = \frac{13}{2}$$
2.
$$2 x - 7 < 0$$
or
$$-\infty < x \wedge x < \frac{7}{2}$$
we get the equation
$$\left(7 - 2 x\right) - 6 = 0$$
after simplifying we get
$$1 - 2 x = 0$$
the solution in this interval:
$$x_{2} = \frac{1}{2}$$
The final answer:
$$x_{1} = \frac{13}{2}$$
$$x_{2} = \frac{1}{2}$$
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
$$\left(2 x - 7\right) - 6 = 0$$
after simplifying we get
$$2 x - 13 = 0$$
the solution in this interval:
$$x_{1} = \frac{13}{2}$$
2.
$$2 x - 7 < 0$$
or
$$-\infty < x \wedge x < \frac{7}{2}$$
we get the equation
$$\left(7 - 2 x\right) - 6 = 0$$
after simplifying we get
$$1 - 2 x = 0$$
the solution in this interval:
$$x_{2} = \frac{1}{2}$$
The final answer:
$$x_{1} = \frac{13}{2}$$
$$x_{2} = \frac{1}{2}$$
Sum and product of roots
[src]
sum
1/2 + 13/2
$$\frac{1}{2} + \frac{13}{2}$$
=
7
$$7$$
product
13 --- 2*2
$$\frac{13}{2 \cdot 2}$$
=
13/4
$$\frac{13}{4}$$
13/4