Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^3=3
-
Equation 5-x^2=0
- Equation (-5*x+3)*(-x+8)=0
-
Equation x^2+6=5x
- Express {x} in terms of y where:
- -6*x+11*y=-5
- -3*x-19*y=-9
- -19*x-15*y=15
- 16*x+14*y=-14
-
Identical expressions
- two *((|x|)+ three)/ three = thirteen *((|x|)- one)/ five
- 2 multiply by (( module of x|) plus 3) divide by 3 equally 13 multiply by ((|x|) minus 1) divide by 5
- two multiply by (( module of x|) plus three) divide by three equally thirteen multiply by ((|x|) minus one) divide by five
- 2((|x|)+3)/3=13((|x|)-1)/5
- 2|x|+3/3=13|x|-1/5
- 2*((|x|)+3) divide by 3=13*((|x|)-1) divide by 5
-
Similar expressions
- 2*((|x|)+3)/3=13*((|x|)+1)/5
- 2*((|x|)-3)/3=13*((|x|)-1)/5
2*((|x|)+3)/3=13*((|x|)-1)/5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2*(|x| + 3) 13*(|x| - 1)
----------- = ------------
3 5
$$\frac{2 \left(\left|{x}\right| + 3\right)}{3} = \frac{13 \left(\left|{x}\right| - 1\right)}{5}$$
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
$$\frac{23}{5} - \frac{29 x}{15} = 0$$
after simplifying we get
$$\frac{23}{5} - \frac{29 x}{15} = 0$$
the solution in this interval:
$$x_{1} = \frac{69}{29}$$
2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$\frac{23}{5} - \frac{29 \left(- x\right)}{15} = 0$$
after simplifying we get
$$\frac{29 x}{15} + \frac{23}{5} = 0$$
the solution in this interval:
$$x_{2} = - \frac{69}{29}$$
The final answer:
$$x_{1} = \frac{69}{29}$$
$$x_{2} = - \frac{69}{29}$$
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
$$\frac{23}{5} - \frac{29 x}{15} = 0$$
after simplifying we get
$$\frac{23}{5} - \frac{29 x}{15} = 0$$
the solution in this interval:
$$x_{1} = \frac{69}{29}$$
2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$\frac{23}{5} - \frac{29 \left(- x\right)}{15} = 0$$
after simplifying we get
$$\frac{29 x}{15} + \frac{23}{5} = 0$$
the solution in this interval:
$$x_{2} = - \frac{69}{29}$$
The final answer:
$$x_{1} = \frac{69}{29}$$
$$x_{2} = - \frac{69}{29}$$
Sum and product of roots
[src]
sum
69 69 - -- + -- 29 29
$$- \frac{69}{29} + \frac{69}{29}$$
=
0
$$0$$
product
-69*69 ------ 29*29
$$- \frac{4761}{841}$$
=
-4761 ------ 841
$$- \frac{4761}{841}$$
-4761/841
Rapid solution
[src]
-69
x1 = ----
29
$$x_{1} = - \frac{69}{29}$$
69
x2 = --
29
$$x_{2} = \frac{69}{29}$$
x2 = 69/29