Desigualdades Líneales. Ejemplo 2.

Understanding Simple Inequalities

Steps to Solve a Simple Inequality

• The instructor, Profe Gabriel, introduces the topic of solving a simple inequality with multiple terms. The first step is to isolate the variable x .

• To isolate x , terms containing variables are kept on one side of the inequality while constant terms are moved to the other side. For example, 4x remains on the left while 3x and constants like 5 and 7 are transferred accordingly.

• After rearranging and simplifying, the expression reduces to x < 12 . The instructor emphasizes that during this process, the direction of the inequality symbol remains unchanged.

Graphical Representation of Solutions

• The graphical solution involves plotting points on a number line. The center point (0) is marked with negative infinity on one side and positive infinity on the other. Since our solution indicates x < 12 , it is represented graphically by shading all values less than 12.

• It’s noted that since x = 12 is included in the solution set, it should be represented as a closed circle at that point on the number line.

Interval Notation for Solutions

• Finally, interval notation is discussed. The left endpoint represents negative infinity (always an open interval), while the right endpoint corresponds to 12 (which is included in this case). Thus, it will be expressed as (-∞, 12].