Question

Which pair of expressions is equivalent for any variable value greater than zero?

Answer 1

D is the only equivalent equation because

b+ b = 2b so they are both the same equation just one is not simplified for b and another is.
2b+3c = 2b + 3c

Answer 2

D. b+b+3c and 2b+3c

Explanation:

The question wants us to find out expressions is equivalent for any variable value greater than zero. So let's analyse all the possible answers to find the correct one.

A. (x+3) and 3x+ 2

If x = 1 , we have:

• (x+3) = 4
• 3x+2 = 5

Both of the two sides are not equivalent

B. 4d+2e and 8d+e

If e=1 and d=1, we have:

• 4d+2e = 8

• 8d+e = 9

Both of the two sides are not equivalent

C. f+f+f+g and 3fg

If f=1 and g=1, we have:

• f+f+f+g = 4

• 3fg = 3

Both of the two sides are not equivalent

D. b+b+3c and 2b+3c

If b=1 and c=1, we have:

• b+b+3c = 5
• 2b+3c = 5

Both of the two sides are equivalent

Or we will simplify the left side: b+b+3c = 2b+3c, hence 2b+3c = 2b+3c are apparent

So we choose D.