How to Solve for Interval with Abs and Max Functions?

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In summary, an interval problem is a mathematical problem involving finding the range of values between two given numbers or satisfying a given inequality. To solve for an interval problem, one must identify the given numbers and use algebraic techniques to find the range of values that satisfy the given conditions. Common mistakes in solving for interval problems include not considering the given conditions and not properly manipulating the equations. An example of solving for an interval problem is finding all values of x that satisfy the inequality 3x + 2 ≤ 10. It is important to solve for interval problems in fields such as physics, chemistry, and biology as it allows us to understand the range of possible values for a variable and make informed decisions.
  • #1
zli034
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Hi all:

The inequality here involves abs, and max functions, how to solve for the interval as show below?
attachment.php?attachmentid=58110&d=1366636107.jpg
 

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  • #2
The very first thing you should probably do is draw the functions.
This will require you to think already about, for example, when the max switches from one expression to the other, and what the abs does here.
 

1. What is an interval problem?

An interval problem is a mathematical problem that involves finding the range of values between two given numbers. It can also refer to finding the values that satisfy a given inequality or set of inequalities.

2. How do you solve for an interval problem?

The first step is to identify the given numbers and determine the relationship between them (e.g. greater than, less than, or equal to). Then, use algebraic techniques such as substitution, manipulation of equations, or graphing to find the range of values that satisfy the given conditions.

3. What are the common mistakes when solving for interval problems?

One common mistake is not considering the given conditions and incorrectly identifying the relationship between the numbers. Another mistake is not properly manipulating the equations or not checking the solutions against the given conditions.

4. Can you give an example of solving for an interval problem?

For example, if the problem asks to find all values of x that satisfy the inequality 3x + 2 ≤ 10, we can subtract 2 from both sides to get 3x ≤ 8. Then, dividing both sides by 3, we get x ≤ 8/3. Therefore, the interval of values that satisfy the inequality is (-∞, 8/3].

5. Why is it important to solve for interval problems?

Solving for interval problems is important in many fields of science, including physics, chemistry, and biology. It allows us to understand the range of possible values for a given variable and make informed decisions based on those values. It also helps us find solutions to real-world problems and make accurate predictions.

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