Jonathan finds a piece of metal that is 2 1/5 inches thick. He files off 3/10 inch. He adds a protective covering to the metal that is 2/10 inch thick. Then, he polishes the metal and removes an additional 1/10 inch. What is the final thickness of the metal?

Step-by-step explanation:

Jonathan finds a piece of metal that is 2  inches thick.

The thickness of the metal = 2 =

He files off  inch,

the thickness becomes =   - =

He adds a protective covering to the metal that is    inch thick.

the thickness becomes,   + =

Then, he polishes the metal and removes an additional inch.

The final thickness becomes, -  = 2 inches

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

2

step-by-step explanation: