Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x+7)*(x-1)=0
-
Equation x/3+x/4=-21
-
Equation sin(x)=0
-
Equation x^3-9*x=0
- Express {x} in terms of y where:
- -2*x+4*y=3
- 3*x-17*y=-6
- 2*x+10*y=-10
- 3*x-2*y=-9
-
Identical expressions
- three *|x|- five , one =| four , two |
- 3 multiply by module of x| minus 5,1 equally |4,2|
- three multiply by module of x| minus five , one equally | four , two |
- 3|x|-5,1=|4,2|
-
Similar expressions
- 3*|x|+5,1=|4,2|
3*|x|-5,1=|4,2| equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
51
3*|x| - -- = |21/5|
10
$$3 \left|{x}\right| - \frac{51}{10} = \left|{\frac{21}{5}}\right|$$
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
$$3 x - \frac{93}{10} = 0$$
after simplifying we get
$$3 x - \frac{93}{10} = 0$$
the solution in this interval:
$$x_{1} = \frac{31}{10}$$
2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$3 \left(- x\right) - \frac{93}{10} = 0$$
after simplifying we get
$$- 3 x - \frac{93}{10} = 0$$
the solution in this interval:
$$x_{2} = - \frac{31}{10}$$
The final answer:
$$x_{1} = \frac{31}{10}$$
$$x_{2} = - \frac{31}{10}$$
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
$$3 x - \frac{93}{10} = 0$$
after simplifying we get
$$3 x - \frac{93}{10} = 0$$
the solution in this interval:
$$x_{1} = \frac{31}{10}$$
2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$3 \left(- x\right) - \frac{93}{10} = 0$$
after simplifying we get
$$- 3 x - \frac{93}{10} = 0$$
the solution in this interval:
$$x_{2} = - \frac{31}{10}$$
The final answer:
$$x_{1} = \frac{31}{10}$$
$$x_{2} = - \frac{31}{10}$$
Sum and product of roots
[src]
sum
31 31 - -- + -- 10 10
$$- \frac{31}{10} + \frac{31}{10}$$
=
0
$$0$$
product
-31*31 ------ 10*10
$$- \frac{961}{100}$$
=
-961 ----- 100
$$- \frac{961}{100}$$
-961/100
Rapid solution
[src]
-31
x1 = ----
10
$$x_{1} = - \frac{31}{10}$$
31
x2 = --
10
$$x_{2} = \frac{31}{10}$$
x2 = 31/10