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

1 Answer
Jul 29, 2015

Answer:

It depends on where the missing right parenthesis goes.

Explanation:

#[4-(7-5(2-3)+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" "# 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.