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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.
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.
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.
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].
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.