My favorite math teacher often shouted "GEMAL says......!" What he means by that is to remember what this acronym means:
- Multiplication & Division
- Addition & Subtraction
- Left to Right
So, when performing the calculation remember to
- respect the parenthesis working from the inside out
- Solve the exponents if there are any, like changing 23 to 8 for example.
- Do multiplication/division before addition/subtraction
- Finally, do addition and subtraction last
- 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.