Answer:
<h2>x = -7</h2>
Step-by-step explanation:
![-2(x+5)=4\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2\!\!\!\!\diagup(x+5)}{-2\!\!\!\!\diagup}=\dfrac{4\!\!\!\!\diagup^2}{-2\!\!\!\!\diagup_1}\\\\x+5=-2\qquad\text{subtract 5 from both sides}\\\\x+5-5=-2-5\\\\x=-7](https://tex.z-dn.net/?f=-2%28x%2B5%29%3D4%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%20%28-2%29%7D%5C%5C%5C%5C%5Cdfrac%7B-2%5C%21%5C%21%5C%21%5C%21%5Cdiagup%28x%2B5%29%7D%7B-2%5C%21%5C%21%5C%21%5C%21%5Cdiagup%7D%3D%5Cdfrac%7B4%5C%21%5C%21%5C%21%5C%21%5Cdiagup%5E2%7D%7B-2%5C%21%5C%21%5C%21%5C%21%5Cdiagup_1%7D%5C%5C%5C%5Cx%2B5%3D-2%5Cqquad%5Ctext%7Bsubtract%205%20from%20both%20sides%7D%5C%5C%5C%5Cx%2B5-5%3D-2-5%5C%5C%5C%5Cx%3D-7)
Answer:
![2a - 3b + 4c = 1](https://tex.z-dn.net/?f=2a%20-%203b%20%2B%204c%20%3D%201)
Step-by-step explanation:
Given
![a^2 + b^2 + c^2 = 2(a - b - c) - 3](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%2B%20c%5E2%20%3D%202%28a%20-%20b%20-%20c%29%20-%203)
Required
Determine ![2a - 3b + 4c](https://tex.z-dn.net/?f=2a%20-%203b%20%2B%204c)
![a^2 + b^2 + c^2 = 2(a - b - c) - 3](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%2B%20c%5E2%20%3D%202%28a%20-%20b%20-%20c%29%20-%203)
Open bracket
![a^2 + b^2 + c^2 = 2a - 2b - 2c - 3](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%2B%20c%5E2%20%3D%202a%20-%202b%20-%202c%20-%203)
Equate the equation to 0
![a^2 + b^2 + c^2 - 2a + 2b + 2c + 3 = 0](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%2B%20c%5E2%20-%202a%20%2B%202b%20%2B%202c%20%2B%203%20%3D%200)
Express 3 as 1 + 1 + 1
![a^2 + b^2 + c^2 - 2a + 2b + 2c + 1 + 1 + 1 = 0](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%2B%20c%5E2%20-%202a%20%2B%202b%20%2B%202c%20%2B%201%20%2B%201%20%2B%201%20%3D%200)
Collect like terms
![a^2 - 2a + 1 + b^2 + 2b + 1 + c^2 + 2c + 1 = 0](https://tex.z-dn.net/?f=a%5E2%20-%202a%20%2B%201%20%2B%20b%5E2%20%2B%202b%20%2B%201%20%2B%20c%5E2%20%20%2B%202c%20%2B%201%20%3D%200)
Group each terms
![(a^2 - 2a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0](https://tex.z-dn.net/?f=%28a%5E2%20-%202a%20%2B%201%29%20%2B%20%28b%5E2%20%2B%202b%20%2B%201%29%20%2B%20%28c%5E2%20%20%2B%202c%20%2B%201%29%20%3D%200)
Factorize (starting with the first bracket)
![(a^2 - a -a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0](https://tex.z-dn.net/?f=%28a%5E2%20-%20a%20-a%20%2B%201%29%20%2B%20%28b%5E2%20%2B%202b%20%2B%201%29%20%2B%20%28c%5E2%20%20%2B%202c%20%2B%201%29%20%3D%200)
![(a(a - 1) -1(a - 1)) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0](https://tex.z-dn.net/?f=%28a%28a%20-%201%29%20-1%28a%20-%201%29%29%20%2B%20%28b%5E2%20%2B%202b%20%2B%201%29%20%2B%20%28c%5E2%20%20%2B%202c%20%2B%201%29%20%3D%200)
![((a - 1) (a - 1)) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0](https://tex.z-dn.net/?f=%28%28a%20-%201%29%20%28a%20-%201%29%29%20%2B%20%28b%5E2%20%2B%202b%20%2B%201%29%20%2B%20%28c%5E2%20%20%2B%202c%20%2B%201%29%20%3D%200)
![((a - 1)^2) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0](https://tex.z-dn.net/?f=%28%28a%20-%201%29%5E2%29%20%2B%20%28b%5E2%20%2B%202b%20%2B%201%29%20%2B%20%28c%5E2%20%20%2B%202c%20%2B%201%29%20%3D%200)
![((a - 1)^2) + (b^2 + b+b + 1) + (c^2 + 2c + 1) = 0](https://tex.z-dn.net/?f=%28%28a%20-%201%29%5E2%29%20%2B%20%28b%5E2%20%2B%20b%2Bb%20%2B%201%29%20%2B%20%28c%5E2%20%20%2B%202c%20%2B%201%29%20%3D%200)
![((a - 1)^2) + (b(b + 1)+1(b + 1)) + (c^2 + 2c + 1) = 0](https://tex.z-dn.net/?f=%28%28a%20-%201%29%5E2%29%20%2B%20%28b%28b%20%2B%201%29%2B1%28b%20%2B%201%29%29%20%2B%20%28c%5E2%20%20%2B%202c%20%2B%201%29%20%3D%200)
![((a - 1)^2) + ((b + 1)(b + 1)) + (c^2 + 2c + 1) = 0](https://tex.z-dn.net/?f=%28%28a%20-%201%29%5E2%29%20%2B%20%28%28b%20%2B%201%29%28b%20%2B%201%29%29%20%2B%20%28c%5E2%20%20%2B%202c%20%2B%201%29%20%3D%200)
![((a - 1)^2) + ((b + 1)^2) + (c^2 + 2c + 1) = 0](https://tex.z-dn.net/?f=%28%28a%20-%201%29%5E2%29%20%2B%20%28%28b%20%2B%201%29%5E2%29%20%2B%20%28c%5E2%20%20%2B%202c%20%2B%201%29%20%3D%200)
![((a - 1)^2) + ((b + 1)^2) + (c^2 + c+c + 1) = 0](https://tex.z-dn.net/?f=%28%28a%20-%201%29%5E2%29%20%2B%20%28%28b%20%2B%201%29%5E2%29%20%2B%20%28c%5E2%20%20%2B%20c%2Bc%20%2B%201%29%20%3D%200)
![((a - 1)^2) + ((b + 1)^2) + (c(c + 1)+1(c + 1)) = 0](https://tex.z-dn.net/?f=%28%28a%20-%201%29%5E2%29%20%2B%20%28%28b%20%2B%201%29%5E2%29%20%2B%20%28c%28c%20%20%2B%201%29%2B1%28c%20%2B%201%29%29%20%3D%200)
![((a - 1)^2) + ((b + 1)^2) + ((c + 1)(c + 1)) = 0](https://tex.z-dn.net/?f=%28%28a%20-%201%29%5E2%29%20%2B%20%28%28b%20%2B%201%29%5E2%29%20%2B%20%28%28c%20%20%2B%201%29%28c%20%2B%201%29%29%20%3D%200)
![((a - 1)^2) + ((b + 1)^2) + ((c + 1)^2) = 0](https://tex.z-dn.net/?f=%28%28a%20-%201%29%5E2%29%20%2B%20%28%28b%20%2B%201%29%5E2%29%20%2B%20%28%28c%20%20%2B%201%29%5E2%29%20%3D%200)
Express 0 as 0 + 0 + 0
![(a - 1)^2 + (b + 1)^2 + (c + 1)^2 = 0 + 0+ 0](https://tex.z-dn.net/?f=%28a%20-%201%29%5E2%20%2B%20%28b%20%2B%201%29%5E2%20%2B%20%28c%20%20%2B%201%29%5E2%20%3D%200%20%2B%200%2B%200)
By comparison
![(a - 1)^2 = 0](https://tex.z-dn.net/?f=%28a%20-%201%29%5E2%20%3D%200)
![(b + 1)^2 = 0](https://tex.z-dn.net/?f=%28b%20%2B%201%29%5E2%20%3D%200)
![(c + 1)^2 = 0](https://tex.z-dn.net/?f=%28c%20%20%2B%201%29%5E2%20%3D%200)
Solving for ![(a - 1)^2 = 0](https://tex.z-dn.net/?f=%28a%20-%201%29%5E2%20%3D%200)
Take square root of both sides
![a - 1 = 0](https://tex.z-dn.net/?f=a%20-%201%20%3D%200)
Add 1 to both sides
![a - 1 + 1 = 0 + 1](https://tex.z-dn.net/?f=a%20-%201%20%2B%201%20%3D%200%20%2B%201)
![a = 1](https://tex.z-dn.net/?f=a%20%3D%201)
Solving for ![(b + 1)^2 = 0](https://tex.z-dn.net/?f=%28b%20%2B%201%29%5E2%20%3D%200)
Take square root of both sides
![b + 1 = 0](https://tex.z-dn.net/?f=b%20%2B%201%20%3D%200)
Subtract 1 from both sides
![b + 1 - 1 = 0 - 1](https://tex.z-dn.net/?f=b%20%2B%201%20-%201%20%3D%200%20-%201)
![b = -1](https://tex.z-dn.net/?f=b%20%3D%20-1)
Solving for ![(c + 1)^2 = 0](https://tex.z-dn.net/?f=%28c%20%20%2B%201%29%5E2%20%3D%200)
Take square root of both sides
![c + 1 = 0](https://tex.z-dn.net/?f=c%20%2B%201%20%3D%200)
Subtract 1 from both sides
![c + 1 - 1 = 0 - 1](https://tex.z-dn.net/?f=c%20%2B%201%20-%201%20%3D%200%20-%201)
![c = -1](https://tex.z-dn.net/?f=c%20%3D%20-1)
Substitute the values of a, b and c in ![2a - 3b + 4c](https://tex.z-dn.net/?f=2a%20-%203b%20%2B%204c)
![2a - 3b + 4c = 2(1) - 3(-1) + 4(-1)](https://tex.z-dn.net/?f=2a%20-%203b%20%2B%204c%20%3D%202%281%29%20-%203%28-1%29%20%2B%204%28-1%29)
![2a - 3b + 4c = 2 +3 -4](https://tex.z-dn.net/?f=2a%20-%203b%20%2B%204c%20%3D%202%20%2B3%20%20-4)
![2a - 3b + 4c = 1](https://tex.z-dn.net/?f=2a%20-%203b%20%2B%204c%20%3D%201)
Answer: a=7
Explanation:
4a+10=38
subtract 10 from both sides
4a=28
divide by 4 on both sides
a=7
Answer:
x = 6
Step-by-step explanation:
-(x - 8) = 2
multiply the negative
-x + 8 = 2
subtract 8 from both sides
-x = -6
x = 6
Answer: 50
Step-by-step explanation:
Let x represent the unknown number
4% × x = 2 or 4/100 × x = 2
25 * (4/100x = 2) * 25
x = 50
Test for x=50
4/100 * 50 = 2
2 = 2
Left side = right side
Therefore, the unknown number is 50