- Identify the correct operation to isolate \(q\): subtract 8 from both sides, which matches option (b).
- Solve the inequality \(q + 8 < 15\) by subtracting 8: \(q < 7\).
- Describe the graph: place an open circle at 7 and draw a ray pointing to the left.
- Final answer: \(\boxed{q < 7}\).
Explanation
- Identifying the correct operation
To solve the inequality \(q + 8 < 15\) for \(q\), we need to isolate the variable \(q\) on one side of the inequality. The term \(8\) is added to \(q\), so we must perform the inverse operation, which is subtraction. Subtracting \(8\) from both sides of the inequality is the correct approach. This corresponds to option (b).
- Solving the inequality
Now, perform the subtraction to solve the inequality:
\[q + 8 < 15\]
\[q + 8 - 8 < 15 - 8\]
\[q < 7\]
Thus, the solution to the inequality is all values of \(q\) less than \(7\).
- Graphing the solution
To graph the inequality \(q < 7\), we use a number line.
- Place an open endpoint at \(7\) on the number line. We use an open circle because the inequality is "strictly less than" (<), meaning \(7\) itself is not included in the solution set.
- Draw a ray extending to the left from the point \(7\). The direction is to the left because we are representing all values of \(q\) that are less than \(7\).
Examples
Imagine you are planning a small gathering and you have a budget constraint. Suppose you have already spent 8 dollars on decorations, and you have a total budget of 15 dollars left to spend on snacks. If \(q\) is the amount you can spend on snacks, the total spending is \(q + 8\). Since your remaining budget is 15 dollars, you must ensure \(q + 8 < 15\). By solving this, you find that you can spend any amount less than 7 dollars on snacks. This simple algebraic process helps in making informed financial decisions daily.