How do you simplify [4-(7-5(2-3)+2]+3[4(75(23)+2]+3?

1 Answer
Jul 29, 2015

It depends on where the missing right parenthesis goes.

Explanation:

[4-(7-5(2-3)+2]+3[4(75(23)+2]+3 is missing a right parenthesis. It could meaningfully go in three places. Each gives a different answer.

Case 1
[4-(7-5color(red)(")")(2-3)+2]+3" "[4(75)(23)+2]+3 do innermost parentheses first

[4-underbrace((7-5)) underbrace((2-3))+2]+3" "

= [4-(2)(-1)+2]+3" " now multiply inside the brackets

= [4-underbrace((2)(-1))+2]+3" "

= [4-(-2)+2]+3" " now add/subtract left to right inside the brackets

= [6+2]+3 = [8]+3 = 11

Case 2

[4-(7-5(2-3)color(red)(")")+2]+3" " innermost parentheses first

[4-(7-5 underbrace((2-3)))+2]+3" "

[4-(7-5(-1))+2]+3" " now multiply -5xx-1

[4-(7+5)+2]+3" " innermost remaining parentheses

[4-12+2]+3" " add/subtract L to R in brackets

[-8+2]+3 = [-6]+3" " finish

= -3

Case 3

[4-(7-5(2-3)+2color(red)(")")]+3

= [4-(7-5(-1)+2color(red)(")")]+3

= [4-(7+5+2color(red)(")")]+3

= [4-(14color(red)(")")]+3

= [-10]+3

= -7

Note Putting the missing right parenthesis outside the brackets would result in a meaningless expression.