2(3r+7)−(2+r) write an equivalent expression a. 4r+12 b. 5r+13 c.5r+12 d.5r-12

Hey there! :) The easiest way to find an expression equivalent to our given one, we can very simply simplify the given expression.

2(3r + 7) - (2 - r)

Simplify.

6r + 14 - 2 - r

Add like terms.

(6r - r) + (14 - 2)

Simplify.

5r + 12

Look at our given answer choices.

Our answer is c. 5r + 12

~Hope I helped!~ 

The Answer is c: 5r+12

Proof:

Simplify the following:
2 (3 r + 7) - (r + 2)

2 (3 r + 7) = 6 r + 14:
6 r + 14 - (r + 2)

-(r + 2) = -r - 2:
14 + 6 r + -r - 2

Grouping like terms, 14 + 6 r - 2 - r = (6 r - r) + (14 - 2):
(6 r - r) + (14 - 2)

6 r - r = 5 r:
5 r + (14 - 2)

 | 1 | 4
- | | 2
 | 1 | 2:

  5 r + 12