Linear functions and Inequalities

Introduction to linear functions and inequalities:

Linear Functions:


In mathematics, the term linear function can refer to either of two different but related concepts:

• a first-degree polynomial function of one variable;
• a map between two vector spaces that preserves vector addition and scalar multiplication.

Inequalities
In mathematics, an inequality is a statement about the relative size or order of two objects or about whether they are the same or not

• The notation a <>less than b.
• The notation a > b means that a is greater than b.
• The notation a ≠ b means that a is not equal to b, but does not say that one is greater than the other or even that they can be compared in size.

linear functions example:

Solve the expression

5(-3y - 2) - (y - 3) = - 4(4y + 5) + 13

Solution:

• Given the equation

5(-3y - 2) - (y - 3) = -4(4y + 5) + 13

• Multiply factors.

-15y - 10 - y + 3 = -16y - 20 +13

• Group like terms.

-16y - 7 = -16y - 7

• Add 16y + 7 to both sides and write the expression as follows

0 = 0

• The above statement is true for all values of y and therefore all real numbers are solutions to the given equation.
Inequalities - Example :
Solve 4x + 3 <>
Solution:
4x + 3 <>
4x +3 – 3 <>
4x <>
4x – 8x <>
- 4x <>
x > – 1
The solution set is {0, 1, 2, 3…}