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

Jul 29, 2015

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

$\left[4 - \underbrace{\left(7 - 5\right)} \underbrace{\left(2 - 3\right)} + 2\right] + 3 \text{ }$

$= \left[4 - \left(2\right) \left(- 1\right) + 2\right] + 3 \text{ }$ now multiply inside the brackets

$= \left[4 - \underbrace{\left(2\right) \left(- 1\right)} + 2\right] + 3 \text{ }$

$= \left[4 - \left(- 2\right) + 2\right] + 3 \text{ }$ now add/subtract left to right inside the brackets

$= \left[6 + 2\right] + 3 = \left[8\right] + 3 = 11$

Case 2

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

$\left[4 - \left(7 - 5 \underbrace{\left(2 - 3\right)}\right) + 2\right] + 3 \text{ }$

$\left[4 - \left(7 - 5 \left(- 1\right)\right) + 2\right] + 3 \text{ }$ now multiply $- 5 \times - 1$

$\left[4 - \left(7 + 5\right) + 2\right] + 3 \text{ }$ innermost remaining parentheses

$\left[4 - 12 + 2\right] + 3 \text{ }$ add/subtract L to R in brackets

$\left[- 8 + 2\right] + 3 = \left[- 6\right] + 3 \text{ }$ 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

$= \left[- 10\right] + 3$

$= - 7$

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