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

case a)

we have that

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

Sample Response: First, combine like terms by combining the variables and constants. Then use properties of equality to isolate the variable and find the value for x.