Answer:
(x-5)
Step-by-step explanation:
factor the equation and the sign is x-5 because the equation has to be negative at the 25.
We need to find the base x in the following equation:
![365_7+43_x=217_{10}](https://tex.z-dn.net/?f=365_7%2B43_x%3D217_%7B10%7D)
First, lets convert 365 from base 7 to base 10. This is given by
![365_7=3\times7^2+6\times7^1+5\times7^0](https://tex.z-dn.net/?f=365_7%3D3%5Ctimes7%5E2%2B6%5Ctimes7%5E1%2B5%5Ctimes7%5E0)
where the upperindex denotes the position of eah number. This gives
![\begin{gathered} 365_7=3\times49+6\times7+5\times1 \\ 365_7=147+42+5 \\ 365_7=194_{10} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20365_7%3D3%5Ctimes49%2B6%5Ctimes7%2B5%5Ctimes1%20%5C%5C%20365_7%3D147%2B42%2B5%20%5C%5C%20365_7%3D194_%7B10%7D%20%5Cend%7Bgathered%7D)
that is, 365 based 7 is equal to 194 bases 10.
Now, lets do the same for 43 based x. Lets convert 43 based x to base 10:
![43_x=4\times x^1+3\times x^0](https://tex.z-dn.net/?f=43_x%3D4%5Ctimes%20x%5E1%2B3%5Ctimes%20x%5E0)
where again, the superindex 0 and 1 denote the position 0 and 1 in the number 43. This gives
![43_x=(4x+3)_{10}](https://tex.z-dn.net/?f=43_x%3D%284x%2B3%29_%7B10%7D)
Now, we have all number in base 10. Then, our first equation can be written in base 10 as
![194_{10}+(4x+3)_{10}=217_{10}](https://tex.z-dn.net/?f=194_%7B10%7D%2B%284x%2B3%29_%7B10%7D%3D217_%7B10%7D)
For simplicity, we can omit the 10 and get
![194+4x+3=217](https://tex.z-dn.net/?f=194%2B4x%2B3%3D217)
so, we can solve this equation for x. By combining similar terms. we have
![197+4x=217](https://tex.z-dn.net/?f=197%2B4x%3D217)
and by moving 197 to the right hand side, we obtain
![\begin{gathered} 4x=217-197 \\ 4x=20 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%204x%3D217-197%20%5C%5C%204x%3D20%20%5Cend%7Bgathered%7D)
Finally, we get
![\begin{gathered} x=\frac{20}{4} \\ x=5 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D%5Cfrac%7B20%7D%7B4%7D%20%5C%5C%20x%3D5%20%5Cend%7Bgathered%7D)
Therefore, the solution is x=5
Answer:
d
Step-by-step explanation:
Hi there!
Since we have 2 variables in the given equation, and you only want to solve for one, the other will end up in your answer.
![6x + 8y = 12](https://tex.z-dn.net/?f=6x%20%2B%208y%20%3D%2012)
Step 1) Add 8y to both sides.
![6x - 8y + 8y = 12 + 8y 6x = 8y + 12](https://tex.z-dn.net/?f=6x%20-%208y%20%2B%208y%20%3D%2012%20%2B%208y%206x%20%3D%208y%20%2B%2012)
Step 2) Divide both sides by 6.
![\frac{6x}{6} = \frac{8y + 12}{6}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6x%7D%7B6%7D%20%3D%20%20%5Cfrac%7B8y%20%2B%2012%7D%7B6%7D%20)
![x = \frac{4}{3} y + 2](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20y%20%2B%202)
Final Answer -
![x = \frac{4}{3} y + 2](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20y%20%2B%202)
Hope this helps! :D
Answer:
x = -1/5
Step-by-step explanation:
2+3 (x+2x) = -2x(2-4) +1
Combine like terms
2+3(3x) = -2x (-2) +1
Distribute
2+9x = 4x +1
Subtract 4x from each side
2+9x-4x = 4x+1-4x
2+5x = 1
Subtract 2 from each sdie
5x = 1-2
5x = -1
Divide by 5
5x/5 = -1/5
x = -1/5