**How To Write An Inequality** – If you’re reading this, you’re probably looking for clarity on how to find all integers (whole numbers) that satisfy an inequality between two numbers. You may have encountered a problem that looks like this:

With an inequality like this, we need to find all possible values of X, our variable. Before we dive in, it’s important to make sure we’re familiar with all the elements of this type of problem. Let’s start by defining some terms and symbols.

## How To Write An Inequality

Now that we’re familiar with all of our terms and symbols, let’s review the above example. We want to find a sequence of numbers that is a solution to:

### Solved: ‘write An Inequality Whose Solutions Are Represented By The Shaded Part Of The Graph M2 Oh Fm’

In this case, X represents the set of numbers that our solution will be. Using what we learned above, let’s put the problem into words. We want to list a sequence of numbers that contains all integers greater than or equal to -2 and less than negative 3. We can visualize this sequence of numbers by thinking of them as if they were on a line. View the image below.

The red line in the image above represents the sequence of numbers that satisfies our inequality. The circle above -2 is filled because -2 is in our set. The circle above 3 is not filled because 3 is not in our set. This is because our set contains all numbers greater than

Knowing this, we can now confidently enumerate the integers that satisfy this inequality by counting from -2 to the last integer before 3. The solution for -2 ≤ X < 3 is -2, -1, 0, 1 and 2.

If you are asked to write down all integers that satisfy the inequality -3 < X ≤ 4, you are looking for all values of X that are greater than -3 and less than or equal to 4. This is because -3 -3 (X is greater than -3) and X ≤ 4 means X is less than or equal to 4.

### December 13th 2018

Since integers are whole numbers, you don’t need to write decimals or fractions. So the integers satisfying -3 < X ≤ 4 are -2, -1, 0, 1, 2, 3, and 4.

Explanation: Here -2 ≤ X X ≥ -2 means, so you want to make a list of all integers greater than or equal to -2. X < 3 means all integers less than 3.

Explanation: here -4 -4, so we want to list all integers greater than -4 but less than 2.

Explanation: This time we have 2X in the middle of the inequality, so the first thing we need to do is divide everything by 2 to isolate our variable. This gives us -3 ≤ X ≤ 2.5

#### Inequality And Interval Notation Chart

3 ≤ X is the same as X ≥ -3, so we want all integers to be greater than or equal to -3. X ≤ 2.5 means we want all integers to be less than or equal to 2.5 (do not include 2.5 in your solution because 2.5 is not an integer).

This content is accurate and truthful to the best of the author’s knowledge and is not intended as a substitute for official and individual advice from a qualified professional.

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