Ch 5 covers solving linear inequalities in one variable (represented on number lines) and two variables (represented as regions in the coordinate plane). Students also solve systems of inequalities.
Solve like equations but reverse the sign when multiplying/dividing by a negative. Solution is an interval. E.g., 2x − 3 > 7 → 2x > 10 → x > 5, i.e., (5, ∞).
A linear inequality ax + by + c ≥ 0 represents a half-plane. To graph: draw the boundary line (solid for ≥, dashed for >), test a point to determine which side to shade.
The solution of a system of inequalities is the intersection of the solution regions. Graphically, this is the region where all half-planes overlap.
Download: https://ncert.nic.in/textbook/pdf/kemh105.pdf | Complete book: https://ncert.nic.in/textbook/pdf/kemh1ps.zip
Consider: 3 < 5. Multiply by −1: −3 and −5. On the number line, −3 is to the right of −5, so −3 > −5. Multiplying by a negative flips the positions on the number line, hence the inequality must reverse.
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