Please help. Thank you!

Question

What is the value of | a-b |+| a-b | if a=b-1/3?

a. 2b+2/3

b. 2b-2/3

c. -2/3

Answer 1

a = b - 1/3

a - b = b-1/3 -b = -1/3

|-1/3| = 1/3

|a-b| = 1/3

|a-b| + |a-b| = 2|a-b| = 2(1/3) = 2/3

b) is false

c) is false due to the negative sign. maybe it's a misprint?

a) is false, unless b = 0

maybe there's a 4th choice? multiple choice problems often have 4 choices

d) is true if it reads 2/3 or if it says none of the above

Answer 2

I'll do the first one for you. You can do the rest. Simply substitute b - 1/3 in place of a:

|a - b| + |a - b|

|b - 1/3 - b| + |b - 1/3 - b|

Rearrange a bit:

|b - b - 1/3| + |b - b - 1/3||

| -1/3 | + | -1/3 |

1/3 + 1/3 = 2/3