# Please, help me understand how these interval problems are solved

• liquidnail
In summary, When simplifying interval expressions, it is important to understand the symbols used. The ∩ symbol means "intersect," which finds numbers that belong to both intervals. The U symbol means "union," which finds numbers that are in either or both intervals. It is also helpful to graph the intervals on a number line to visualize the solution. Google can be a useful resource for finding online explanations and examples.
liquidnail

## Homework Statement

simplify:

1. (-∞, -2) ∩ [-2, ∞)

2. (-∞, 5] ∩ [5, ∞)

3. (-∞, 5) U (4, ∞)

4. (-∞, 5) ∩ (3, ∞)

## The Attempt at a Solution

It has been so long since I last saw a problem set like that. Honestly, I don't even remember how these problems should be solved. The text I am using just gives the definition and quickly glosses over since intervals are not the primary aim of it.
Would someone be so kind as to explain how I should go about solving these problems. Many thanks.

liquidnail said:

## Homework Statement

simplify:

1. (-∞, -2) ∩ [-2, ∞)
The ∩ symbol means "intersect," which means the numbers that belong to both intervals. What numbers are less than -2 AND greater than or equal to -2?

Another approach is to draw the two intervals on the number line, to see which numbers are in both intervals.
liquidnail said:
2. (-∞, 5] ∩ [5, ∞)

3. (-∞, 5) U (4, ∞)
The U symbol means "union," which means the numbers that are in the first interval OR are in the second interval. A number belongs to the union of two intervals if it is in either or both intervals.
liquidnail said:
4. (-∞, 5) ∩ (3, ∞)

## The Attempt at a Solution

It has been so long since I last saw a problem set like that. Honestly, I don't even remember how these problems should be solved. The text I am using just gives the definition and quickly glosses over since intervals are not the primary aim of it.
Would someone be so kind as to explain how I should go about solving these problems. Many thanks.

liquidnail said:
$\small(-\infty,-2)\normalsize\:\bigcap\; \small{[-2,\infty)}$
An open interval has its end point denoted by a round parenthesis: (

A closed interval has its end point denoted by a square bracket: [

## 1. What are interval problems?

Interval problems are mathematical problems that involve finding the range of values between two given points. These points can be numbers, variables, or expressions.

## 2. How are interval problems solved?

Interval problems are solved by first identifying the given points and then finding the range of values between them. This can be done by using algebraic methods, such as solving equations or inequalities, or by graphing the given points and finding the range visually.

## 3. What is the purpose of solving interval problems?

The purpose of solving interval problems is to determine the possible values within a given range. This can be useful in many real-life situations, such as determining the possible range of values for a stock price or finding the possible solutions to a system of equations.

## 4. What are some common strategies for solving interval problems?

Some common strategies for solving interval problems include using the properties of inequalities, such as adding or subtracting the same number to both sides, or using the distributive property to combine like terms. Graphing the given points and visually determining the range can also be an effective strategy.

## 5. Are there any tips for solving interval problems more efficiently?

One tip for solving interval problems more efficiently is to first simplify the given expressions or equations before attempting to find the range. This can make the problem easier to understand and solve. Additionally, practicing and familiarizing oneself with different methods for solving interval problems can also improve efficiency.

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