Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation y³-2y²+y-2=0
- Equation |4x+1|=0
- Equation √3ctgx+3=0
-
Equation log(4/(7-x))/log(x^2)=5
- Express {x} in terms of y where:
- 17*x+16*y=7
- 17*x-11*y=2
- -12*x+3*y=-9
- 15*x-17*y=19
-
Identical expressions
- |4x+ one |= zero
- module of 4x plus 1| equally 0
- module of 4x plus one | equally zero
- |4x+1|=O
-
Similar expressions
- (|4*x+1|)=(|-2-x|)+2
- |4x-1|=0
|4x+1|=0 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.
$$4 x + 1 \geq 0$$
or
$$- \frac{1}{4} \leq x \wedge x < \infty$$
we get the equation
$$4 x + 1 = 0$$
after simplifying we get
$$4 x + 1 = 0$$
the solution in this interval:
$$x_{1} = - \frac{1}{4}$$
2.
$$4 x + 1 < 0$$
or
$$-\infty < x \wedge x < - \frac{1}{4}$$
we get the equation
$$- 4 x - 1 = 0$$
after simplifying we get
$$- 4 x - 1 = 0$$
the solution in this interval:
$$x_{2} = - \frac{1}{4}$$
but x2 not in the inequality interval
The final answer:
$$x_{1} = - \frac{1}{4}$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$4 x + 1 \geq 0$$
or
$$- \frac{1}{4} \leq x \wedge x < \infty$$
we get the equation
$$4 x + 1 = 0$$
after simplifying we get
$$4 x + 1 = 0$$
the solution in this interval:
$$x_{1} = - \frac{1}{4}$$
2.
$$4 x + 1 < 0$$
or
$$-\infty < x \wedge x < - \frac{1}{4}$$
we get the equation
$$- 4 x - 1 = 0$$
after simplifying we get
$$- 4 x - 1 = 0$$
the solution in this interval:
$$x_{2} = - \frac{1}{4}$$
but x2 not in the inequality interval
The final answer:
$$x_{1} = - \frac{1}{4}$$
Sum and product of roots
[src]
sum
-1/4
$$- \frac{1}{4}$$
=
-1/4
$$- \frac{1}{4}$$
product
-1/4
$$- \frac{1}{4}$$
=
-1/4
$$- \frac{1}{4}$$
-1/4