- Analyze the given inequality \(q - 8 < 12\).
- Recognize that the goal is to isolate \(q\) by performing the inverse operation to subtract \(8\), which is adding \(8\) to both sides.
- Perform the addition: \(q - 8 + 8 < 12 + 8\), resulting in \(q < 20\).
- Conclude that option \(b\) is the correct step, given by \(\boxed{b}\).
Explanation
- Analysis of the Inequality
The given inequality is \(q - 8 < 12\). Our goal is to isolate the variable \(q\) on one side of the inequality. This will allow us to determine the range of values that satisfy the condition. To do this, we need to perform an algebraic operation that removes the constant term \(-8\) from the left side of the inequality.
- Solving the Inequality
The expression on the left side is \(q - 8\). To isolate \(q\), we must perform the inverse operation of subtraction, which is addition. By adding \(8\) to both sides of the inequality, we maintain the balance of the expression and effectively eliminate the \(-8\). This process is governed by the property of inequalities that states adding the same constant to both sides preserves the inequality. Applying this, we get:
\[q - 8 + 8 < 12 + 8\]
\[q < 20\]
This shows that the necessary step to solve the inequality is to add \(8\) to both sides.
- Conclusion
Comparing our finding with the given options:
ASubtract 8 from both sides of the inequality.
BAdd 8 to both sides of the inequality.
CAdd 12 to both sides of the inequality.
DSubtract 12 from both sides of the inequality.
Our calculation confirms that option (b) is the correct procedure. The final answer is \(\boxed{b}\).
Examples
Imagine you have a budget of \(\$12\) left for school supplies, and you already spent \(\$8\) on a notebook. Let \(q\) be the original amount of money you had. The relationship between your original money, the spent amount, and the remaining budget can be expressed as \(q - 8 < 12\). To find out the original amount you had, you need to add the \(\$8\) spent back to the \(\$12\) you have left, which is exactly how we solve this inequality. Understanding these operations is essential for managing personal finances, planning budgets, and solving various real-world problems involving missing quantities.