Lesson Notes By Weeks and Term v4 - SHS 2
APPLICATION OF ALGEBRA
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APPLICATION OF ALGEBRA
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Subject: Additional Mathematics
Class: SHS 2
Term: 1st Term
Week: 9
Grade code: 2.1.1.LI.6
Strand code: 1
Sub-strand code: 1
Content standard code: 2.1.1.CS.3
Indicator code: 2.1.1.LI.6
Theme: MODELLING WITH ALGEBRA
Subtheme: APPLICATION OF ALGEBRA
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This lesson focuses on solving systems of linear inequalities, which are essential tools for decision-making in real-life situations involving constraints like budgets, time, or resources. In Ghana, a small business owner deciding how many items to produce, a student managing their weekly budget for food and data, or a farmer planning their planting schedule all face problems that can be modelled and solved using inequalities. This lesson moves from abstract algebra to visual, graphical solutions that make complex problems easier to understand and solve. We will learn how to translate real-world problems into mathematical language and find the 'best' solutions graphically.
2.1. What is a Linear Inequality?
A linear equation in two variables (e.g., `2x + y = 10`) represents a single straight line. All the points on that line are solutions to the equation.
A linear inequality in two variables (e.g., `2x + y ≤ 10`) represents an entire region on the Cartesian plane. It uses one of the following symbols: ` ` : greater than `≤` : less than or equal to `≥` : greater than or equal to
The solution to a linear inequality is not just a line, but all the points on one side of that line.