Quadratic inequalities have more than one solution, and one of the solving options is to add or subtract a similar number on each side of the equation. Find the solutions to the unknown variables. A solution to a quadratic inequality refers to a number that makes the equation a true statement when it replaces the variable. You can choose a number that is already in the equation, as seen in the example below.
To solve the inequality x -- 2 > 5, add 2 on each side of the equation to get x > 7.
Switch the sides of the equation and change the signs used in the original equation. If an equation has a greater-than sign, you can include a less-than sign to make it easier for you to get a solution, as seen in the example below.
The equation 5 -- x > 4 can be solved by switching it, to give x < 1. In this example, the greater-than sign has been switched to a less-than sign.
Multiply or divide the number in the equation on each side. You can choose to divide or multiply it as a positive or negative number. If you choose to multiply it as a negative number, the inequality sign also needs to change. When you use this rule to solve the equation, it is not possible to divide using the variable because it is unknown. The example below will help to make this rule clearer.
The inequality equation 2x ≤ 6 can be solved by dividing each of these sides by 2 to get x ≤ 3.
The inequality equation -2x ≤ 6 can be solved by dividing it by -2 on each side to get x ≥ - 3. In this example, the greater-than sign has been changed to a less-than sign because a negative number was used in the division.
One side has to be equated to zero. This is used to separate the positive numbers from the negative ones. If an expression in the equation is greater than zero, it has a positive sign. If an expression is less than zero, it has a negative sign. It is only possible to determine this when one of the sides in the equation is zero, as seen in the example below.
The equation x2 + 4 -- 4x ≥ is converted into x2 - 4x - 5 ≥ 0
A quadratic inequality needs to have a boundary point when you are solving it. The boundary point is used to mark exactly where an equation is equal to zero. Once you determine a boundary point, it becomes easier for you to solve a quadratic inequality.