Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -6x+2=-x+22
- Equation x^2-x-72=0
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Equation x-5(x+3)=5
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Equation 5x+8=-12
- Express {x} in terms of y where:
- 7*x-2*y=18
- -10*x-12*y=-10
- -2*x+2*y=4
- 11*x+8*y=-16
-
Identical expressions
- 6x- five / seven =2x- one / three +2x1-x/ twenty-one
- 6x minus 5 divide by 7 equally 2x minus 1 divide by 3 plus 2x1 minus x divide by 21
- 6x minus five divide by seven equally 2x minus one divide by three plus 2x1 minus x divide by twenty minus one
- 6x-5 divide by 7=2x-1 divide by 3+2x1-x divide by 21
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Similar expressions
- 6x-5/7=2x+1/3+2x1-x/21
- 6x+5/7=2x-1/3+2x1-x/21
- (6*x-5)/7=(2*x-1)/3+2
- (6*x-5)/7=2*(x-1)/3+2
- 6x-5/7=2x-1/3+2x1+x/21
- 6x-5/7=2x-1/3-2x1-x/21
6x-5/7=2x-1/3+2x1-x/21 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
x
6*x - 5/7 = 2*x - 1/3 + 2*x1 - --
21
$$6 x - \frac{5}{7} = - \frac{x}{21} + \left(2 x_{1} + \left(2 x - \frac{1}{3}\right)\right)$$
Detail solution
Given the linear equation:
Looking for similar summands in the right part:
Move free summands (without x)
from left part to right part, we given:
$$6 x = \frac{41 x}{21} + 2 x_{1} + \frac{8}{21}$$
Move the summands with the unknown x
from the right part to the left part:
$$6 x + \left(-2\right) x_{1} = \frac{41 x}{21} + \frac{8}{21}$$
Divide both parts of the equation by (-2*x1 + 6*x)/x
We get the answer: x = 8/85 + 42*x1/85
6*x-5/7 = 2*x-1/3+2*x1-x/21
Looking for similar summands in the right part:
-5/7 + 6*x = -1/3 + 2*x1 + 41*x/21
Move free summands (without x)
from left part to right part, we given:
$$6 x = \frac{41 x}{21} + 2 x_{1} + \frac{8}{21}$$
Move the summands with the unknown x
from the right part to the left part:
$$6 x + \left(-2\right) x_{1} = \frac{41 x}{21} + \frac{8}{21}$$
Divide both parts of the equation by (-2*x1 + 6*x)/x
x = 8/21 + 41*x/21 / ((-2*x1 + 6*x)/x)
We get the answer: x = 8/85 + 42*x1/85
The graph
Rapid solution
[src]
8 42*re(x1) 42*I*im(x1)
x1 = -- + --------- + -----------
85 85 85
$$x_{1} = \frac{42 \operatorname{re}{\left(x_{1}\right)}}{85} + \frac{42 i \operatorname{im}{\left(x_{1}\right)}}{85} + \frac{8}{85}$$
x1 = 42*re(x1)/85 + 42*i*im(x1)/85 + 8/85
Sum and product of roots
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sum
8 42*re(x1) 42*I*im(x1) -- + --------- + ----------- 85 85 85
$$\frac{42 \operatorname{re}{\left(x_{1}\right)}}{85} + \frac{42 i \operatorname{im}{\left(x_{1}\right)}}{85} + \frac{8}{85}$$
=
8 42*re(x1) 42*I*im(x1) -- + --------- + ----------- 85 85 85
$$\frac{42 \operatorname{re}{\left(x_{1}\right)}}{85} + \frac{42 i \operatorname{im}{\left(x_{1}\right)}}{85} + \frac{8}{85}$$
product
8 42*re(x1) 42*I*im(x1) -- + --------- + ----------- 85 85 85
$$\frac{42 \operatorname{re}{\left(x_{1}\right)}}{85} + \frac{42 i \operatorname{im}{\left(x_{1}\right)}}{85} + \frac{8}{85}$$
=
8 42*re(x1) 42*I*im(x1) -- + --------- + ----------- 85 85 85
$$\frac{42 \operatorname{re}{\left(x_{1}\right)}}{85} + \frac{42 i \operatorname{im}{\left(x_{1}\right)}}{85} + \frac{8}{85}$$
8/85 + 42*re(x1)/85 + 42*i*im(x1)/85