Answer: The simplified form of 6(x-5)-(5-x)+35 is 5x + 10.
Explanation:
To simplify the expression 6(x-5)-(5-x)+35, we can follow the order of operations (PEMDAS/BODMAS):
1. Start by simplifying the parentheses (x-5) and (5-x):
- For (x-5), we leave it as it is since there are no like terms to combine.
- For (5-x), we can rewrite it as (-1)(x-5) using the distributive property.
2. Next, simplify the expression inside the parentheses:
- (x-5) remains the same.
- (-1)(x-5) can be rewritten as -x + 5 by distributing the -1 to both terms inside the parentheses.
3. Now, we can substitute these simplified expressions back into the original expression:
6(x-5) - (5-x) + 35 becomes 6(x-5) - (-x + 5) + 35.
4. Continue simplifying:
- Distribute 6 to (x-5), resulting in 6x - 30.
- Distribute -1 to (-x + 5), resulting in x - 5.
- Simplify -(-x + 5) to x - 5 by removing the double negative.
5. Combine like terms:
6x - 30 - (x - 5) + 35 becomes 6x - 30 - x + 5 + 35.
Combining like terms, we get 5x + 10.
6. Finally, we have the simplified expression:
5x + 10