Answer: (14/21n - 14n - 4)/7.
I hope this helps you and everyone on here. :)
Explanation:
To simplify the expression 2/3n + 2(-n - 2/7), we need to follow the order of operations (PEMDAS/BODMAS). Let's break it down step-by-step:
1. Start with the expression within the parentheses: -n - 2/7. To subtract a fraction from a whole number, we need to convert the whole number into a fraction with a denominator of 1. So, -n can be written as -n/1. Now, we have (-n/1) - (2/7).
2. To subtract fractions, we need to have a common denominator. In this case, the common denominator is 7. So, we rewrite the expression as (-n * 7/7) - (2/7).
3. Simplifying further, we get (-7n/7) - (2/7), which equals (-7n - 2)/7.
4. Now, let's substitute this simplified expression back into the original expression: 2/3n + 2(-7n - 2)/7.
5. Next, we multiply 2 by (-7n - 2), which gives us (-14n - 4)/7.
6. Now, the expression becomes 2/3n + (-14n - 4)/7.
7. To add or subtract fractions, we need a common denominator. In this case, the common denominator is 21. So, we rewrite the expression as (2/3n * 7/7) + (-14n - 4)/7.
8. Simplifying further, we get (14/21n + (-14n - 4)/7).
9. Combining the fractions, we have (14/21n - 14n - 4)/7.
10. Finally, we can combine like terms by multiplying 14/21n by 1/1 (which doesn't change its value), resulting in (14/21n - 14n - 4)/7.
So, the simplified expression is (14/21n - 14n - 4)/7.