 Inequations must be mastered by students in the third grade. For this purpose, this course on solving first degree inequalities with one unknown in the third grade (3ème) will be of great help to you. In this chapter, we will study the definition as well as the method of solution and the solution set given on a graduated line.

## I. First degree inequalities with one unknown

Definition:

An inequation is an inequality between two expressions with letters called unknowns.

Examples:  Definition:

Solving an inequation with unknown x is to determine all values of x (if any) for which the inequality is true. Each of these values is called the solution of the inequation.

## II. solve an inequation of the first degree

Properties:
• You do not change the meaning of an inequality when you add (or subtract) the same number to each member of the inequation;
• The direction of an inequality is not changed when we multiply (or divide) each member of the inequation by a positive non-zero number.
• The direction of an inequality is changed by multiplying (or dividing) each member of the inequation by a non-zero negative number.

Examples:

Solve the following inequations:  ## III. Solving problems with inequalities

Her current average is 13.7 out of 20.

What is the minimum score she must achieve on her next assignment for her average to become 14 or higher?

2. To transport signs, a company wishes to compare the rates of two companies:

The company “Vitlivré” proposes a sum of 3.20 € per kilometer travelled, while the company “Rapido” proposes a fixed price of 180 € and a sum of 2 € per kilometer travelled.

a.Which company should be chosen for a 100 km transport?

b. From what mileage is the “Rapido” company the most interesting?

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