Solve the following algebraic expression: [5z-(x+2y)]-[3x-(y-2z)]

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Greetings.  This algebraic expression (incidentally, what's the difference between an expression and an equation? Answer follows) requires you to see that a negative sign can be interpreted as (-1) and distributed using the Distributive Property of Multiplication.

Using the problem-solving strategy of "Simplify and Solve," we first look to determine...

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Greetings.  This algebraic expression (incidentally, what's the difference between an expression and an equation? Answer follows) requires you to see that a negative sign can be interpreted as (-1) and distributed using the Distributive Property of Multiplication.

Using the problem-solving strategy of "Simplify and Solve," we first look to determine if we can combine similar terms.  Not yet. So, let's address those nasty (-) minus signs.  To eliminate the confusion that they create, shall we change all operation signs to (+) addition signs?  Let's do that:

[5z + -1(x + 2y)] + -1[3x + -1(y + -2z)]

= 5z + -1x + -2y + -1[3x + -1y + 2z]

= 5z + -1x + -2y + -3x + 1y + -2z   Now we combine similar terms

=  -4x + -y + 3z

(Oh yes!  An expression does not include an equal sign, but an equation does include an equal sign).

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Note:

Many algebra textbooks suggest that variables should written in alphabetical order with decreasing exponents with secondary variables having increasing exponents. For example,

x^2 +2xy + y^2 is proper; however

y^2  + x^2 +2xy  is not.

For the original problem described above, a better answer would be

- 4x - y + 3z

instead of demanding that the first term always be positive.

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This problem is about moving the minus sign inside the parenthesis so that order of operations is preserved.

[5z-(x+2y)]-[3x-(y-2z)]

5z - x - 2y - (3x - y + 2z)

5z - x - 2y - 3x + y - 2z

3z - 4x - y

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