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Simplify $ 11x - \left[ {8y - \left\{ {11x - \left( {7z - 3y} \right) + 5y - \left( {3x - 2y - z} \right)} \right\}} \right] $

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Last updated date: 18th Jun 2024
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Answer
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Hint: Simplify the above expression based upon the priority order. Parentheses (round brackets) have the highest priority then the square brackets and then the curly brackets. This means, the terms in the round brackets must be solved first and then the terms in square brackets and then the terms in curly brackets. Use this info to simplify the expression. `

Complete step-by-step answer:
We are given to simplify the expression $ 11x - \left[ {8y - \left\{ {11x - \left( {7z - 3y} \right) + 5y - \left( {3x - 2y - z} \right)} \right\}} \right] $
The expression has terms composed in square brackets, curly brackets and round brackets.
Following the order of priority, the part of the expression with round brackets must be solved first and then the part of the expression with square brackets and then the part of the expression with curly brackets.
First we are solving for the round brackets.
There is a minus sign before the part of the expression with round brackets. So send the minus sign inside.
$ \Rightarrow 11x - \left[ {8y - \left\{ {11x - \left( {7z - 3y} \right) + 5y - \left( {3x - 2y - z} \right)} \right\}} \right] = 11x - \left[ {8y - \left\{ {11x - 7z + 3y + 5y - 3x + 2y + z} \right\}} \right] $
The expression now has only square brackets and curly brackets. So, the next one is the part with square brackets. But there is a sub part with curly brackets inside the square brackets. So solve the curly brackets first.
There is a minus sign before the part of the expression with curly brackets. So send the minus sign inside.
 $ \Rightarrow 11x - \left[ {8y - \left\{ {11x - 7z + 3y + 5y - 3x + 2y + z} \right\}} \right] = 11x - \left[ {8y - 11x + 7z - 3y - 5y + 3x - 2y - z} \right] $
Now we are solving for square brackets by sending the minus sign inside.
 $ \Rightarrow 11x - \left[ {8y - 11x + 7z - 3y - 5y + + 3x - 2y - z} \right] = 11x - 8y + 11x - 7z + 3y + 5y - 3x + 2y + z $
Now we are putting the similar terms together.
 $
\Rightarrow 11x + 11x - 3x - 8y + 3y + 5y + 2y - 7z + z \\
   = 19x + 2y - 6z \;
 $
Therefore, the simplification of $ 11x - \left[ {8y - \left\{ {11x - \left( {7z - 3y} \right) + 5y - \left( {3x - 2y - z} \right)} \right\}} \right] $ is $ 19x + 2y - 6z $
So, the correct answer is “ $ 19x + 2y - 6z $ ”.

Note: If we solve square brackets first and then round brackets next, then the result obtained by doing so will be wrong. So always the order must be followed. And round brackets must be solved first. If there is a presence of another type of brackets, say x, composed in round brackets, x must be solved and then we should go for round brackets.