Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 25*x^2=16
- Equation 3*x^2-48=0
-
Equation x^2-5*x+7=0
-
Equation x^2-20=0
- Express {x} in terms of y where:
- 1*x+11*y=-3
- 10*x+3*y=2
- -20*x+14*y=16
- 15*x-3*y=19
- Derivative of:
- 3|x|
- Graphing y =:
- 3|x|
- 3|x|
-
Identical expressions
- four |-x|- five (|x|- four)= three |x|
- 4 module of minus x| minus 5(|x| minus 4) equally 3|x|
- four module of minus x| minus five (|x| minus four) equally three |x|
- 4|-x|-5|x|-4=3|x|
-
Similar expressions
- 2*((|x|)+3)/3=13*((|x|)-1)/5
- 3*|x|-5,1=|4,2|
- x*|x|+3*|x|+6+2*x=3
- 4|+x|-5(|x|-4)=3|x|
- 4|-x|-5(|x|+4)=3|x|
- 4|-x|+5(|x|-4)=3|x|
4|-x|-5(|x|-4)=3|x| equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
4*|-x| - 5*(|x| - 4) = 3*|x|
$$- 5 \left(\left|{x}\right| - 4\right) + 4 \left|{- x}\right| = 3 \left|{x}\right|$$
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
$$20 - 4 x = 0$$
after simplifying we get
$$20 - 4 x = 0$$
the solution in this interval:
$$x_{1} = 5$$
2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$20 - 4 \left(- x\right) = 0$$
after simplifying we get
$$4 x + 20 = 0$$
the solution in this interval:
$$x_{2} = -5$$
The final answer:
$$x_{1} = 5$$
$$x_{2} = -5$$
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
$$20 - 4 x = 0$$
after simplifying we get
$$20 - 4 x = 0$$
the solution in this interval:
$$x_{1} = 5$$
2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$20 - 4 \left(- x\right) = 0$$
after simplifying we get
$$4 x + 20 = 0$$
the solution in this interval:
$$x_{2} = -5$$
The final answer:
$$x_{1} = 5$$
$$x_{2} = -5$$
Sum and product of roots
[src]
sum
-5 + 5
$$-5 + 5$$
=
0
$$0$$
product
-5*5
$$- 25$$
=
-25
$$-25$$
-25