Select the best answer for the question.
7. Simplify and solve this equation for [tex]$q: 3 q+5+2 q-5=65$[/tex].
A. [tex]$q=15$[/tex]
B. [tex]$q=13$[/tex]
C. [tex]$q=23$[/tex]
D. [tex]$a=11$[/tex]
Answer (2)
Combine like terms: 3 q + 2 q + 5 − 5 = 65 simplifies to 5 q = 65 .
Divide both sides by 5: 5 5 q = 5 65 .
Solve for q : q = 13 .
The solution is 13 .
Explanation
Simplifying the Equation First, we need to simplify the given equation by combining like terms. The equation is: 3 q + 5 + 2 q − 5 = 65
Combining Like Terms Combine the terms with q : 3 q + 2 q = 5 q Combine the constant terms: 5 − 5 = 0 So the simplified equation is: 5 q = 65
Solving for q Now, to solve for q , we need to isolate q by dividing both sides of the equation by the coefficient of q , which is 5: 5 5 q = 5 65 q = 13
Comparing to Answer Choices Therefore, the solution to the equation is q = 13 . Now we compare our solution to the answer choices provided.
Examples
Imagine you're baking cookies for a bake sale. You need a total of 65 cookies. You already baked some, and you know that for every batch you bake, you get 3 chocolate chip cookies and 2 oatmeal cookies. You also added 5 sprinkles and then removed 5 (because you sneezed!). How many batches do you need to bake to reach your goal of 65 cookies? This problem is similar to solving the equation, where 'q' represents the number of batches you need to bake.
The simplified equation from 3 q + 5 + 2 q − 5 = 65 results in q = 13 . The correct answer from the given options is B: q = 13 .
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