Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation exp(x)=0
-
Equation 2*x^2+5*x-25=13*x+17
-
Equation 3*x-15=0
-
Equation 0=2-3x
- Express {x} in terms of y where:
- 9*x-19*y=-20
- 15*x+17*y=-10
- -11*x-18*y=6
- -7*x-5*y=-17
-
Identical expressions
- two / three *((one / two)*z-(six / five))- four *((eleven / ten)*z- two)= three *(one / six *z- three)+ two *z+ ten
- 2 divide by 3 multiply by ((1 divide by 2) multiply by z minus (6 divide by 5)) minus 4 multiply by ((11 divide by 10) multiply by z minus 2) equally 3 multiply by (1 divide by 6 multiply by z minus 3) plus 2 multiply by z plus 10
- two divide by three multiply by ((one divide by two) multiply by z minus (six divide by five)) minus four multiply by ((eleven divide by ten) multiply by z minus two) equally three multiply by (one divide by six multiply by z minus three) plus two multiply by z plus ten
- 2/3((1/2)z-(6/5))-4((11/10)z-2)=3(1/6z-3)+2z+10
- 2/31/2z-6/5-411/10z-2=31/6z-3+2z+10
- 2 divide by 3*((1 divide by 2)*z-(6 divide by 5))-4*((11 divide by 10)*z-2)=3*(1 divide by 6*z-3)+2*z+10
-
Similar expressions
- 2/3*((1/2)*z+(6/5))-4*((11/10)*z-2)=3*(1/6*z-3)+2*z+10
- 2/3*((1/2)*z-(6/5))+4*((11/10)*z-2)=3*(1/6*z-3)+2*z+10
- 2/3*((1/2)*z-(6/5))-4*((11/10)*z-2)=3*(1/6*z-3)-2*z+10
- 2/3*((1/2)*z-(6/5))-4*((11/10)*z-2)=3*(1/6*z+3)+2*z+10
- 2/3*((1/2)*z-(6/5))-4*((11/10)*z+2)=3*(1/6*z-3)+2*z+10
- 2/3*((1/2)*z-(6/5))-4*((11/10)*z-2)=3*(1/6*z-3)+2*z-10
2/3*((1/2)*z-(6/5))-4*((11/10)*z-2)=3*(1/6*z-3)+2*z+10 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/z 6\
2*|- - -|
\2 5/ /11*z \ /z \
--------- - 4*|---- - 2| = 3*|- - 3| + 2*z + 10
3 \ 10 / \6 /
$$\frac{2 \left(\frac{z}{2} - \frac{6}{5}\right)}{3} - 4 \left(\frac{11 z}{10} - 2\right) = \left(2 z + 3 \left(\frac{z}{6} - 3\right)\right) + 10$$
Detail solution
Given the linear equation:
Expand brackets in the left part
Expand brackets in the right part
Looking for similar summands in the left part:
Looking for similar summands in the right part:
Move free summands (without z)
from left part to right part, we given:
$$- \frac{61 z}{15} = \frac{5 z}{2} - \frac{31}{5}$$
Move the summands with the unknown z
from the right part to the left part:
$$\frac{\left(-197\right) z}{30} = - \frac{31}{5}$$
Divide both parts of the equation by -197/30
We get the answer: z = 186/197
2/3*((1/2)*z-(6/5))-4*((11/10)*z-2) = 3*(1/6*z-3)+2*z+10
Expand brackets in the left part
2/3*1/2z-6/5)-4*11/10z-2) = 3*(1/6*z-3)+2*z+10
Expand brackets in the right part
2/3*1/2z-6/5)-4*11/10z-2) = 3*1/6*z-3*3+2*z+10
Looking for similar summands in the left part:
36/5 - 61*z/15 = 3*1/6*z-3*3+2*z+10
Looking for similar summands in the right part:
36/5 - 61*z/15 = 1 + 5*z/2
Move free summands (without z)
from left part to right part, we given:
$$- \frac{61 z}{15} = \frac{5 z}{2} - \frac{31}{5}$$
Move the summands with the unknown z
from the right part to the left part:
$$\frac{\left(-197\right) z}{30} = - \frac{31}{5}$$
Divide both parts of the equation by -197/30
z = -31/5 / (-197/30)
We get the answer: z = 186/197
Sum and product of roots
[src]
sum
186 --- 197
$$\frac{186}{197}$$
=
186 --- 197
$$\frac{186}{197}$$
product
186 --- 197
$$\frac{186}{197}$$
=
186 --- 197
$$\frac{186}{197}$$
186/197