Linear Inequalities: Introduction
Prerequisite knowledge
The chapters Numbers, Algebra, 2-Dimensional geometry: nodes and lines and 2-Dimensional geometry: conic sections are necessary for a good understanding of this chapter. We will also use the calculation rules for inequalities quite a lot. These were covered in the theory section of the chapter Planning of real numbers.
If #x#, #y# and #z# are real numbers. Then the following laws apply:
- Exactly one of the three statements "#x\gt y#" "#x\lt y#" "#x=y#" is true
- If #x\lt y# and #y\lt z#, then #x\lt z#
- If #x\gt y#, then #x+z\gt y+z#
- If #x\gt y#, then #-x\lt -y#
- If #x\gt y# and #z\gt0#, then #z\,x\gt z\,y#
- If #x\gt0# and #y\gt 0#, then #x\,y \gt 0#
- If #x\gt0#, then #\frac{1}{x}\gt 0 #
- If #x\gt y\ge0#, then #x^2\gt y^2# and #\sqrt{x}\gt\sqrt{y}#
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