What are the two equations created by the inequality $|x-12|+5<27$?
y1 = [ ] and y2 = [ ]
Answer (2)
The two equations created by the inequality ∣ x − 12∣ + 5 < 27 are y 1 = ∣ x − 12∣ + 5 and y 2 = 27 . This means that the expression on the left must be less than the value on the right. Therefore, we have defined both parts of the inequality clearly.
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Identify the left-hand side of the inequality: y 1 = ∣ x − 12∣ + 5 .
Identify the right-hand side of the inequality: y 2 = 27 .
The two equations are y 1 = ∣ x − 12∣ + 5 and y 2 = 27 .
The final answer is y 1 = ∣ x − 12∣ + 5 and y 2 = 27 .
Explanation
Understanding the Problem We are given the inequality ∣ x − 12∣ + 5 < 27 . Our goal is to identify the two equations, y 1 and y 2 , that represent the left-hand side and the right-hand side of the inequality, respectively.
Defining the First Equation The left-hand side of the inequality is ∣ x − 12∣ + 5 , so we can define the first equation as y 1 = ∣ x − 12∣ + 5 .
Defining the Second Equation The right-hand side of the inequality is 27 , so we can define the second equation as y 2 = 27 .
Final Answer Therefore, the two equations are y 1 = ∣ x − 12∣ + 5 and y 2 = 27 .
Examples
Imagine you're planning a road trip and want to keep your travel time within a certain range. The absolute value inequality helps you determine how much earlier or later you can leave and still arrive on time. For instance, if you want to arrive by 5 PM, the inequality can help you calculate the latest and earliest departure times, considering potential traffic delays or unexpected stops. This concept is useful in project management, scheduling, and any situation where you need to stay within specific boundaries or timeframes.
