Final answer:
Factoring -3x-9 can be done by extracting the GCF, resulting in -3(x + 3), or understanding the multiplication rules for signs, where the common factor -3 is taken out because -3x and -9 share it. Maintaining balance in equations is crucial during such operations.
Step-by-step explanation:
There are two different ways of factoring the expression -3x-9. The first method involves taking out the greatest common factor (GCF), which in this case is -3. Here's how you can do it:
- Factor out the GCF: -3(x + 3).
- Check by distributing the -3 back into the parentheses to make sure you get the original expression.
The second method deals with understanding the rules of signs in multiplication and division:
- If -3x is considered to be -3 * x, and -9 as -3 * 3, then the common -3 can be factored out.
Remember, when dealing with factoring, it's essential to keep the balance on both sides of the equation. Whether you are multiplying both sides by a factor, or subtracting a term from both sides, it's critical to apply the operation equally to maintain equality, as shown in the shared reference material. Also, the reference material highlights concepts such as multiplying numbers with the same or opposites signs, as well as dealing with negative exponents. These concepts all support the fundamental principle that operations done to one side of an equation must be done to the other.