Please help me with this it's worth 80 points and please show all work
3x - 4 + 6x = -31

17 = 3x - 10

2x + 6 = 4x - 8

17x - 5(3x - 11) = 41

5x - (3x - 6) = 18

6x - 3(4 - 5x) = 30

x - (-5) = 7

This is a lot of questions-

I did them all on a calculator.

1.)

3x - 4 + 6x = -31

3x + 6x - 4 = -31

9x - 4 = -31

9x = -27

x= -3

2.)

17 = 3x - 10

3x -10 = 17

-10 = -10

3x = 27

divide both sides by 3

x= 9

3.)

2x + 6 = 4x - 8

-6 = -6

2x = 4x -14

-4x (both sides)

-2x = -14

divide both sides by -2

x = 7

4.)

17x - 5(3x - 11) = 41

2x +55 = 41

-55 (both sides)

2x = -14

divide 2 both sides

x = -7

5.)

5x - (3x - 6) = 18

2x + 6 = 18

-6 both sides

2x = 12

divide both sides by 2

x = 6

6.)

6x - 3(4 - 5x) = 30

21 - 12 = 30

+12 boh sides

21x = 42

divide both sides by 21

x = 2

7.)

x - (-5) = 7

x + 5 = 7

-5 both sides

x = 2

true? is that what you're asking or do you mean something else?

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer:   (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))