What is an Inequality
An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. Example: 2 > 1.
What the symbols mean
An inequality has 1 out of 4 different signs. The first sign is >, which is the greater than sign. This sign is used when the number on the left is bigger than the on the right. The second sign is <, which is the less than sign. A less than sign is used when the number on the left is smaller than the number on the right. The third sign is ≥, which is the greater than or equal to sign. This sign is used when the number on the left can be greater or equal to the number on the right. The fourth sign is ≤, which is the less than or equal to sign. This sign is placed when the number on the left is less than or equal to the number on the right. Examples: 3 > 2, 7 < 8, x ≥ 13, 9 ≤ x.
How to solve
Solving inequalities is almost exactly like solving an equation; legal moves. The only difference is when you are dividing by a negative, you need to flip the sign. Example, if you have -3x < 21, after you divide and get x < -7 you need to flip the sign, so your answer becomes x > -7
How to graph an inequality
To graph an inequality on a number line, you need to know how to identify what the sign is. If the sign is < or > than you will put an open dot on your graph and if the sign is ≤, or ≥, you will place a closed dot on your graph. Once you know what kind of dot you need, you need to find the number that is the inequality with x. For example x > 10. You would find 10 on your number line. Once you have found 4 draw the dot on top of the 4. The direction your arrow goes depends on the sign. For our example, x > 4 the arrow would go to the right of 4. This is saying that x can be any number to the right of 4.
How to check an inequality
Since solving inequalities are very similar to solving equations, checking is also mainly the same. To check your solution, you replace the variable with your answer. Example: 2x+4 > 8. When you do all your legal moves you end up with x > 2. From here, your answer should be 2. Now you replace the variable with 2 and solve. 2(2) + 4 > 8 turns into 4 + 4 > 8, then 8 > 8.Now you know that your number is right. There is also a second to check and inequality. The second way to check is to make sure the sign is going the right way. To do this you need to put any number that is greater than 2 into the question. Example: 2(10) + 4 > 8 turns into 24 > 8 which is a correct statement.