Simplify: 8q+3q-6t+2q-4q

Simplify: 8q+3q-6t+2q-4q

The correct answer and explanation is:

To simplify the expression 8q + 3q – 6t + 2q – 4q, follow these steps:

1. Identify like terms: Like terms are terms that contain the same variable raised to the same power. In this case, the terms 8q, 3q, 2q, and -4q all involve the variable q. The term -6t is a different type of term because it contains the variable t, so it cannot be combined with the q terms.
2. Combine like terms: To simplify the expression, combine the q terms together:
   • 8q + 3q + 2q – 4q
   • First, add the coefficients (the numbers in front of the q’s): 8 + 3 = 11, then 11 + 2 = 13, and finally 13 – 4 = 9.
   So, the simplified expression for the q terms is 9q.
3. Write the final expression: Now, write the result from combining the q terms along with the remaining term, which is -6t:
   • The final expression is 9q – 6t.

Explanation:

Simplifying an algebraic expression involves combining like terms, which makes the expression shorter and easier to work with. In this case, the terms involving q are added or subtracted based on their coefficients, and since the term -6t does not share the same variable, it remains unchanged. By identifying the terms that can be combined, you reduce the expression to its simplest form. This process is fundamental in algebra, as it allows for easier manipulation of expressions and equations in problem-solving situations.