Which expression is equivalent to the expression below? 4q+4r+q+q+q
The correct answer and explanation is:
To simplify the expression 4q+4r+q+q+q4q + 4r + q + q + q, we need to combine like terms.
Step 1: Identify like terms
The expression has two types of terms: those that involve qq and those that involve rr. We can group them as follows:
- 4q+q+q+q4q + q + q + q (all terms involving qq)
- 4r4r (term involving rr)
Step 2: Combine like terms
- The terms involving qq are 4q4q, qq, qq, and qq. To combine these, add the coefficients of qq: 4q+1q+1q+1q=(4+1+1+1)q=7q4q + 1q + 1q + 1q = (4 + 1 + 1 + 1)q = 7q
- The term involving rr is already simplified as 4r4r, so it remains as is.
Step 3: Rewrite the expression
After combining the like terms, the simplified expression is: 7q+4r7q + 4r
Final Answer:
The expression equivalent to 4q+4r+q+q+q4q + 4r + q + q + q is 7q+4r7q + 4r.
Explanation:
Simplifying algebraic expressions often involves combining terms that have the same variable. In this case, qq is the variable that appears in multiple terms, and we add their coefficients to find the total coefficient for qq. The term with rr remains unchanged because it is not like the terms involving qq. This process of combining like terms helps make expressions easier to work with and solve.