Urgente!! Quien sabe hallar el valor de x?

Question

6) 8(x + 2) = 3(x - 5) - 7(x + 3) 

7) a(x + 1) + 5a(x - 1) = 2(3b - 2a) 

8) x(a + 1) - x(a - 1) = 2a + 4 

9) (x + 2)(x - 5) = (x - 1)(x - 6) 

10) (x - 8)(x + 1) = (x + 5)(x - 3) 

11) (x + 1)(6x - 2) = (2x + 4)(3x + 2) 

12) 2(x - 2)(x + 3) - (2x + 4)(x - 2) = 0

Answer 1

6)

Given equation

8(x + 2) = 3(x - 5) - 7(x + 3)

Distribute terms using distributive property:  a( b + c) = ab + ac.

8*x + 8*2 = 3*x - 3*5 - 7*x - 7*3

8x + 16 = 3x - 15 - 7x - 21

8x + 16 = - 4x - 36

Seperate variables and constant terms.

8x + 4x = - 16 - 36

12x = - 52

x = - 52 / 12

x = -13/3

Answer 2

7)

Given equation

a(x + 1) + 5a(x - 1) = 2(3b - 2a) 

Distribute terms using distributive property:  a( b + c) = ab + ac.

a*x + a*1 + 5a*x - 5a*1 = 2*3b - 2*2a

ax + a + 5ax - 5a = 6b - 4a

6ax - 4a = 6b - 4a

6ax = 6b - 4a + 4a

Seperate variables and constant terms.

6ax = 6b

x = 6b / 6a

x = b / a

Answer 3

8)

Given equation

x(a + 1) - x(a - 1) = 2a + 4

x(a + 1) - x(a - 1) = 2a + 2*2

Take common term using distributive property:  ab + ac = a( b + c)

x [ (a + 1) - (a - 1) ] = 2(a + 2)

x [ a + 1 - a + 1 ] = 2(a + 2)

x [  1 + 1 ] = 2(a + 2)

x [ 2 ] = 2(a + 2)

2x = 2(a + 2)

x = 2(a + 2) / 2

x = a + 2

Answer 4

9)

Given equation

(x + 2)(x - 5) = (x - 1)(x - 6)

Distribute terms using distributive property:  a( b - c) = ab - ac.

x(x - 5) + 2(x - 5) = x(x - 6) - 1(x - 6)

(x*x - x*5 + 2*x - 2*5) = (x*x - x*6 - 1*x + 1*6)

(x² - 5x + 2x - 10) = (x² - 6x - x + 6)

(x² - 5x + 2x - 10) = (x² - 6x - x + 6)

(x² - 3x - 10) = (x² - 7x + 6)

Seperate variables and constant terms.

x² - 3x + 7x - x²=  6 + 10

4x = 16

x = 16 / 4

x = 4

Answer 5

10)

Given equation

(x - 8)(x + 1) = (x + 5)(x - 3)

Distribute terms using distributive property:  a( b - c) = ab - ac.

x(x + 1) - 8(x + 1) = x(x + 5) - 3(x + 5)

(x*x + x*1 - 8*x - 8*1) = (x*x + x*5 - 3*x - 3*5)

(x² + x - 8x - 8) = (x² + 5x - 3x - 15)

(x² - 7x - 8) = (x² + 2x - 15)

Seperate variables and constant terms.

x² - 7x - 2x - x²=  -15 + 8

- 9x = -7

x = -7 / (-9)

x = 7/9

Answer 6

12)

Given equation

2(x - 2)(x + 3) - (2x + 4)(x - 2) = 0

Take out term (x - 2) as common term.

(x - 2) [ 2(x + 3) - (2x + 4) ] = 0

(x - 2) [ 2*x + 2*3 - 2x - 4 ] = 0

(x - 2) [ 2x + 6 - 2x - 4 ] = 0

(x - 2) [  6 - 4 ] = 0

2(x - 2) = 0

x - 2 = 0

x = 2

Answer 7

11)

Given equation

(x + 1)(6x - 2) = (2x + 4)(3x + 2)

Distribute terms using distributive property :  a( b - c) = ab - ac.

6x(x + 1) - 2(x + 1) = 3x(2x + 4) + 2(2x + 4)

6x*x + 6x*1 - 2*x - 2*1 = 3x*2x + 3x*4 + 2*2x + 2*4

6x² + 6x - 2x - 2 = 6x² + 12x + 4x + 8

6x² + 4x - 2 = 6x² + 16x + 8

Seperate variables and constant terms.

6x² + 4x - 6x² - 16x = + 8 + 2

4x - 16x = + 8 + 2

-12x = 10

12x = - 10

x = - 10 / 12

x = -5/6