Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sinx=1
-
Equation x^2+5*x-14=0
-
Equation -2*x-7=-4*x
-
Equation x+4|x|=3
- Express {x} in terms of y where:
- 7*x+6*y=-1
- 16*x+6*y=11
- 10*x+8*y=3
- 6*x+18*y=-18
-
Identical expressions
- x+ four |x|= three
- x plus 4 module of x| equally 3
- x plus four module of x| equally three
-
Similar expressions
- x-4|x|=3
x+4|x|=3 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.
$$x \geq 0$$
or
$$0 \leq x \wedge x < \infty$$
we get the equation
$$x + 4 x - 3 = 0$$
after simplifying we get
$$5 x - 3 = 0$$
the solution in this interval:
$$x_{1} = \frac{3}{5}$$
2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$4 \left(- x\right) + x - 3 = 0$$
after simplifying we get
$$- 3 x - 3 = 0$$
the solution in this interval:
$$x_{2} = -1$$
The final answer:
$$x_{1} = \frac{3}{5}$$
$$x_{2} = -1$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x \geq 0$$
or
$$0 \leq x \wedge x < \infty$$
we get the equation
$$x + 4 x - 3 = 0$$
after simplifying we get
$$5 x - 3 = 0$$
the solution in this interval:
$$x_{1} = \frac{3}{5}$$
2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$4 \left(- x\right) + x - 3 = 0$$
after simplifying we get
$$- 3 x - 3 = 0$$
the solution in this interval:
$$x_{2} = -1$$
The final answer:
$$x_{1} = \frac{3}{5}$$
$$x_{2} = -1$$
Sum and product of roots
[src]
sum
-1 + 3/5
$$-1 + \frac{3}{5}$$
=
-2/5
$$- \frac{2}{5}$$
product
-3 --- 5
$$- \frac{3}{5}$$
=
-3/5
$$- \frac{3}{5}$$
-3/5
The graph