Final answer:
The simplest form of the expression (5(x-3)-3(2x+4))/9 is (-x/9) - 3, achieved by using the distributive property and then combining like terms before dividing each term by the denominator.
Step-by-step explanation:
The student is asking for help simplifying the algebraic expression (5(x-3)-3(2x+4))/9. To simplify this expression, first expand the numerator by applying the distributive property:
5(x-3) becomes 5x - 15
-3(2x+4) becomes -6x - 12
Combine the like terms to get a simplified numerator:
5x - 15 - 6x - 12 = -x - 27
Now the expression is (-x - 27)/9.
Each term in the numerator can be divided by the denominator :
(-x/9) - (27/9) which simplifies to (-x/9) - 3.
This is the simplest form of the given expression.