Example of Factorizable Inequality

An inequality is the relationship that exists between two algebraic expressions to indicate that they can be different or equal depending on the type in question, greater than (>), less than ( =), less than or equal to (<=).

The solution to this relationship is the set of values ​​that a variable can take to satisfy the inequality.

The properties of an inequality are as follows:

• If a> b and b> c then a> c.
• If the same number is added to both sides of an inequality, it holds a> b then a + c> b + c.
• If both sides of an inequality are multiplied by the same number, the inequality holds. If a> b then ac> bc.
• If a> b then –a
• If a> b then 1 / a <1 / b.

With these properties it is possible to solve a factorable inequality, factoring its terms and finding the set of values ​​of the variable that meet it.

Example of Factorizable Inequality:

Let the following inequality be

x2 + 6x + 8> 0

Factoring the expression on the left we have:

(x + 2) (x + 4)> 0

For this inequality to hold for all real numbers such that

x It must be greater than -2, since for x <= -2 the result is the set of numbers less than or equal to 0.

Find the set of numbers that satisfy the following inequality:

(2x + 1) (x + 2)

Carrying out the operations we have to:

2x2 + 3x + 2

Subtracting x2 from both sides of the inequality is:

2x2 - x2 + 3x + 2

x2 + 3x + 2 <3x

subtracting 3x from both sides of the inequality we have:

x2 + 3x - 3x + 2 <3x - 3x

x2 + 2 <0

then

x2 <2

x <2/21

The set of numbers that solves this problem is all those numbers that are less than the square root of 2.