Simplifying Algebraic Expressions

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To simplify the expression 4[12-3(8-5)]-1, the correct order of operations must be followed, starting with the innermost parentheses. The expression simplifies to 4[12 - 3(3)] - 1, which further simplifies to 4[3] - 1, resulting in 12 - 1 = 11. For the second expression, 5x-3{2x-2[x-2(1-x)]}, the same principles apply, requiring careful handling of parentheses and operations. The discussion emphasizes the importance of correctly applying the order of operations to achieve accurate simplification. Properly simplifying these algebraic expressions is crucial for solving related problems effectively.
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Homework Statement


simplify 4[12-3(8-5)]-1

and simplify 5x-3{2x-2[x-2(1-x)]}


Homework Equations





The Attempt at a Solution

 
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The attempt at a solution, please.
 


Norway said:
The attempt at a solution, please.

I haven't reviewed any algebra for years so I don't remeber how could this be simplified.

what i tried was

in 4[12-3(8-5)]-1 I just tried to sovle 4[ 9(3)]-1 = 4[27]-1 = 4 [26] = 104
but I guess that's not what i was told to do.
 


The first one is just arithmetic - not algebra.

4[12 - 3(8 - 5)] - 1

Take care of the operations inside of parentheses or brackets first, then multiplications, and finally additions/subtractions.

In particular 12 - 3(8 -5) is not equal to 9(8 - 5).

Keep the same ideas in mind for the second problem.
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...

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