Math in general is not an easy thing for everyone. In math, inequality is probably one of the things that a lot of people think is hard to solve. Even the quite simple question like “Which graph represents the inequality X ≤ –2 or X ≥ 0?” can be hard, especially for those who have no idea about the subject.
If you are one of those people who are having a hard time finding out the answer to the question above, you come to the right place as you will be given the correct answer about it. Here is the answer to the question “Which graph represents the inequality X ≤ –2 or X ≥ 0?”:
There are a total of two inequalities that are given. The first one is x ≥ 0 and the second one is x ≤ -2. Since, we have to take all the values greater than or equal to 0 and all the values less than or equal to -2. So, we reject the values lying between -2 and 0 i.e. we will not take the values from (-2, 0). So, plotting the given inequality gives the following graph:
In the world of math, the term inequality is used to call a statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to, between two numbers or algebraic expressions. It is possible for the inequalities to be posed either as questions, similar to equations. Not only that, it is also possible for them to be solved by similar techniques, or as statements of facts in the form of theorems. For instance, according to triangle one, the sum of the lengths of any two sides of a triangle is greater than or equal to the length of the remaining side. In fact, mathematical analysis relies on things like that in the proofs of its most important theorems.
Talking about the inequalities, sometimes, it will be needed for you to solve them like these:
| Symbol | Words | Example |
| > | Greater than | X + 3 > 2 |
| < | Less than | 7x < 28 |
| ≥ | Greater than or equal to | 5 ≥ x – 1 |
| ≤ | Less than or equal to | 2y + 1 ≤ 7 |
The main purpose of inequality is to have X, or any variable, on its own on the left of the inequality sign. It is something like x < 5 or y ≥ 11. It is called solved. Here is the example: x + 2 > 12. You can subtract 2 from both sides: x + 2 – 2 > 12 – 2. When it is simplified, it becomes x > 10.
How do you solve the inequalities? Solving the inequalities is the same as solving equations. Most of the things are the same. However, there is a difference, which is to pay more attention to the direction of the inequality. There are a total of four things that are able to change the direction, including:
- < becomes >
- > becomes <
- ≤ becomes ≥
- ≥ becomes ≤
It should be noted that there are a few things that do not affect the direction of the inequality, such as:
- Adding or subtracting a number from both sides
- Multiplying or dividing both sides by a positive number
- Simplifying a side
For instance: 3x < 7 + 3. It is able to be simplified 7 + 3 without affecting the inequality: 3x < 10.
On the other hands, these followings are the things that are able to change the direction of the inequality:
- Multiplying or dividing both sides by a negative number
- Swapping left and right hand sides
For instance: 2y + 7 < 12. When it is swapped left and right hand sides, the direction of the inequality also must be changed: 12 > 2y + 7.
Apparently, it is possible for you to solve the inequalities by adding or subtracting a number from both sides just like x + 3 < 7. If both sides are subtracted, the thing becomes x + 3 – 3 < 7 – 3. From there, it can be concluded that the solution is x < 4. If you have no idea about it, it means x can be any value less than 4.
What do you do: You went from x + 3 < 7 to x < 4. This one works properly by adding and subtracting. The reason is because if the same amount from both sides are added or subtracted, it does not affect the inequality. For instance, Kay Lee has more coins compared to Nemanja Matic. If both Kay Lee and Nemanja Matic get three more coins each, Kay Lee will still have more coins compared to Nemanja Matic.
What if the x is on the right when solving it? Actually, this kind of thing does not matter. You can just swap sides. However, it is important to reverse the sign so it still points at the right value. For instance: 12 < x + 5. If it is subtracted from both sides, it becomes 12 – 5 < x + 5 – 5. The solution to the question is 7 < x. The normal one is to actually put the x on the left hand side. To do that, you can just flip the sides and the inequality sign. The solution before can become x > 7.
Apart from that, another thing that you do is to multiply or to divide both sides by a value, just like in algebra multiplying. Please be a bit more careful.
For the positive value, feel free to multiply or divide a thing by a positive number. For instance: 3y < 15. If it is divided on both sides by 3, the result will be 3y /3 < 15 / 3. From that, the solution can be y < 5.
What about the negative number? When a thing is multiplied or divided by a negative number, it is a must to reverse the inequality.
