Final answer:
To simplify (3x - 5) - (4x + 6), we must first change the signs of the terms in the second parentheses due to subtraction, resulting in 3x - 5 - 4x - 6. When combining like terms, we get -x - 11 as the simplified expression.
Step-by-step explanation:
To simplify the expression (3x - 5) - (4x + 6), we need to subtract the terms in the second parentheses from the terms in the first. It's important to reverse the sign of each term in the second parentheses because of the subtraction operation. So the expression becomes 3x - 5 - 4x - 6. Combining like terms, we subtract 4x from 3x to get -x, and -5 from -6 to get -11. The simplified expression is -x - 11.
Following the rules of adding and subtracting numbers with different signs:
- If we subtract a positive number, we change its sign to negative.
- If we subtract a negative number, we change its sign to positive.
- For like terms, after adjusting for signs, simply combine them using addition or subtraction.
In conclusion, by changing the signs and combining like terms, we arrive at the simplified form of the given algebraic expression.