Desigualdades dobles. Ejemplo 4.

Double Inequalities Exercise

Introduction to Double Inequalities

• The video begins with an introduction to double inequalities, emphasizing the importance of understanding different types of solutions and methods for solving them.

Solving the Double Inequality

• The process starts by isolating terms on both sides of the inequality, specifically addressing how to handle addition and subtraction. The example involves subtracting 7 from both sides while maintaining the inequality symbol.

• As part of the solution, it is noted that when dividing by a negative number, the direction of the inequality symbol must be reversed. This is crucial in obtaining accurate results.

Graphical Representation

• A graphical approach is introduced after deriving algebraic solutions, illustrating how to represent inequalities on a number line from negative infinity to positive infinity. The value '8' is highlighted as a critical point in this representation.

Conditions for Solutions

• Two conditions are established: x leq 0 and x geq 8 . These conditions dictate where values fall on the number line—values less than or equal to zero are placed on one side while those greater than or equal to eight are placed on another side.

Union of Solution Sets

• It is explained that since not all conditions can be satisfied simultaneously within certain intervals (e.g., between 0 and 8), we need to consider unions of sets for complete solutions:

• From negative infinity to zero (open at zero)

• From eight to positive infinity (closed at eight).

This union represents all valid solutions graphically.