Final answer:
The algebraic expression 4y + 13x - 5 + 6y - x simplifies to 10y + 12x - 5. Answers must be evaluated according to whether they are fully simplified, equivalent but not fully simplified, or not equivalent to the given expression.
Step-by-step explanation:
The student's task is to simplify the algebraic expression 4y + 13x - 5 + 6y - x. Simplifying an algebraic expression means to combine like terms and reduce the expression to the simplest form possible. First, combine like terms, which are terms that have the same variable raised to the same power. In this case, we combine the terms with y and the terms with x.
Let's simplify step-by-step:
- Combine the y terms: 4y + 6y = 10y.
- Combine the x terms: 13x - x = 12x.
- The constant -5 doesn't combine with any other term, so it remains as is.
- Putting it all together, we get the simplified expression: 10y + 12x - 5.
Now, let's evaluate the students' answers:
- -5 + 22xy is Not equivalent; it introduces a new term 22xy which was not in the original expression.
- 14x -5 + 10y is Equivalent, but not fully simplified; the terms are equivalent but in a different order, and the coefficient of x is incorrect.
- 17y - 5 + 5x is Not equivalent; the coefficient of y is incorrect.
- 13x - 5 + 10y - x is Equivalent, but not fully simplified; it contains the correct terms but has not combined the x terms.
- 4y + 12x - 5 + 6y is Equivalent, but not fully simplified; it is the original expression before simplifying.
- 12x - 5 + 10y is Equivalent and simplified fully; it is the correct simplified form of the original expression.