Final answer:
The expression (4x + 7) - (-3x - 9) + 9x - 28 simplifies to 16x - 12. It can be factored by taking out the greatest common factor of 4, giving the factored form as 4(4x - 3). The factored form is checked by redistributing the 4 to ensure the original expression is accurately simplified.
Step-by-step explanation:
To simplify the expression (4x + 7) - (-3x - 9) + 9x - 28, we first need to remove the parentheses. We can do this by changing the signs of the terms inside the parentheses that we're subtracting:
- (4x + 7) becomes 4x + 7
- -(-3x - 9) becomes +3x + 9
Now combine the like terms:
4x + 7 + 3x + 9 + 9x - 28
This simplifies to:
16x - 12
Since the expression is a linear combination of terms, it cannot be factored further unless we factor out common terms. Here, we can factor out the greatest common factor, which is 4:
4(4x - 3)
Therefore, the simplified and factored form is 4(4x - 3).