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

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3 Answers

My favorite math teacher often shouted "GEMAL says......!" What he means by that is to remember what this acronym means:

  1. Grouping
  2. Exponents
  3. Multiplication & Division
  4. Addition & Subtraction
  5. Left to Right

So, when performing the calculation remember to

  1. respect the parenthesis working from the inside out
  2. Solve the exponents if there are any, like changing 23 to 8 for example.
  3. Do multiplication/division before addition/subtraction
  4. Finally, do addition and subtraction last
  5. Within a given pair of parenthesis, do the above from left to right.

 This explanation doesn't account for variable X but I thought to still share this as it has served me well over the years.

Separate the 2 parts of the problem: 3(2(x-3)+2) and 5(x-3)

Starting with 3(2(x-3)+2), distribute the first 2 to x-3:

2(x-3) = 2x-6

Now you have: 3(2x-6+2)

Add 2 to -6: 3(2x-4)

Distribute the 3: 6x-12

Now you can work on the other part of the problem, 5(x-3).

Distribute the 5 to x-3: 5x-15

Put the 2 pieces back together: 6x-12+5x-15

Simplify it to get the answer: 11x-27

Always work with the parenthesis first: so 

work with the (2(x-3)+2)first and then the 5(x-3)

then work out the like variables (2x-6+2) then,  use the distributive property on 3(2x-4). Then, work through all the like variables for your final answer. 

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

3(2x-6+2)+(5x-15)

3(2x-4)+(5x-15)

6x-12+5x-15

=11x-27