Describe the steps used to find the value of x in the equation x + (2x + 40) + (3x – 50) = 15,002.

Reorder the terms:

(x+2x+3x)+(40-50)=15,002

Combine like terms:

x+2x+3x=6x

40-50=-10

6x-10=15,002

adds +10 both sides

6x-10+10=15,002+10

Combine like terms:

-10+10=0

15,002+10=15,012

6x=15,012

divide by 6 both sides

x=15,012/6

x=2,502

the answer is

x=2,502

case b)

we have that
X + (2x + 40) + (3x – 50) = 15,002

 Reorder the terms: 

X + (40 + 2x) + (3x + -50) = 15002 

 Remove parenthesis around (40 + 2x)

 X + 40 + 2x + (3x + -50) = 15002 

Reorder the terms: 

X + 40 + 2x + (-50 + 3x) = 15002 

Remove parenthesis around (-50 + 3x) 

X + 40 + 2x + -50 + 3x = 15002 

Reorder the terms: 

40 + -50 + X + 2x + 3x = 15002 

Combine like terms:

 40 + -50 = -10 

-10 + X + 2x + 3x = 15002 

 Combine like terms: 

2x + 3x = 5x

 -10 + X + 5x = 15002 

 Solving

 -10 + X + 5x = 15002 

Solving for variable 'X'

. Move all terms containing X to the left, all other terms to the right. Add '10' to each side of the equation.

 -10 + X + 10 + 5x = 15002 + 10

 Reorder the terms:

 -10 + 10 + X + 5x = 15002 + 10 

 Combine like terms: 

-10 + 10 = 0 

0 + X + 5x = 15002 + 10 

X + 5x = 15002 + 10 

 Combine like terms:

 15002 + 10 = 15012

 X + 5x = 15012  

Add '-5x' to each side of the equation.

 X + 5x + -5x = 15012 + -5x 

 Combine like terms:

 5x + -5x = 0 

X + 0 = 15012 + -5x 

X = 15012 + -5x 

 Simplifying 

X = 15012 + -5x

the answer is

X=15,012-5x

10 - 8 = -2

  8 - 6 = -2

etc, so -2 is the common difference

step-by-step explanation: