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Inequalities are similar to equations, you have to solve for a variable (X, Y, Z , A, B, etc...), the main difference is that with an equation you are solving for only one value (X=3, Z=4, A=-9, etc) with an inequality you are solving for a range of numbers, that means that you variable can be a number greater than, less than, greater or equal than to, less or equal than to...
For Example: If X > 3 (X is greater than 3) , X can be any value from 3.1, 3.2, 5, 7, 900, 1000 and so on.
Let's remember the symbols for inequalities
Greater than >
Less than <
Greater than or equal to ≥
Less than or equal to ≤
- Step 2
Solve the inequality like a regular equation
We have the inequality 3(X-4) ≤ X - 6. Let's solve for "X" , that means to leave "X" alone. We can solve this like a regular equation.
- Step 3
Solve the Parenthesis
First we need to remember PEMDAS (Please Excuse My Dear Aunt Sally). We have to solve for the parenthesis. Let's multiply 3 times X, and 3 times -4
- Step 4
Move the variables to the left side
Once we do the parenthesis, 3x - 12 ≤ X -6, let's move the "X" from the right to the left side, we do this by adding "X" to both sides.
- Step 5
Move the numbers to the right side
Our inequality looks like this 2X - 12 ≤ X -6. Now we have to move -12 from the left to the right side, let's add 12 to both sides.
- Step 6
Divide by 2 both sides
Our main goal is to leave "X" alone, 2 is multiplying X, let's eliminate him from the left side by dividing both sides by 2
- Step 7
Final Answer
Our result is X ≤ 3, that means that the value of X has to be a number less than or equal to the number 3. For example 3, 2, 1, 0 -1, -2, -3 and so on. We can also write our answer like this (-∞, 3], we use always parenthesis for the infinitive symbol , and we use a bracket because our inequality is less than or equal to. If our equation was 3(X-4) < X -6, then our answer would be ( -∞, 3) with a parenthesis, this means that X can not be 3, it has to be less than 3, for example 2.99, 2.50, 0, -1, -2, -3 . Conclusion. If you have an inequality with the equal symbol (≤≥) , you have to use the bracket [], if you have the inequality without the equal symbol (<>), then you have to use parenthesis (
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