Module 5 (Linear Inequalities) LINEAR INEQUALITIES for solving Linear Inequalities The following rules can be applied to any inequality Add or subtract the same n umber or expressions to both the sides. Multiply or divide both the sides by same positive number The inequality reverses if it is multiplied or divide by a negative number a < b b > a a < b 1/a > 1/b x2 a2 x a and x -a ≤ ≤ ≥ Points to remember x = 0 is y-axis y = 0 is x-axis x = k is a line parallel to y-axis passing through (k, 0) of x-axis. y = k is a line parallel to x-axis passing through (0, k) of y-axis. Method to find Graphical Solution Draw lines corresponding to each equation treating it as equality. Find the feasible region: intersection of all the inequalities. LEVEL I – Solve 24x < 100 when x is a natural number. Solve the inequalities and draw the graph of the solution on number line: 3x 2 < 2x – + 1. Solve the following system of inequalities: 2x + y 8, x + 2y 10. ≥ ≥ the following system of inequalities graphically: x 3, y 2. ≥ ≥ the following system of inequalities graphically: x + y 9, y>x, x≥0. ≤ Find all of consecutive odd positive integers both of which are smaller than 10 such that there sum is more than 11. LEVEL II – the inequalities and draw the graph of the solution on number line: 5(2x 7) 3(2x + 3) 0. – – ≤ the following system of inequalities graphically: x + y 400, 2x + y 600. ≤ ≤
Module 5 (Linear Inequalities) LINEAR INEQUALITIES for solving Linear Inequalities The following rules can be applied to any inequality Add or subtract the same n umber or expressions to both the sides. Multiply or divide both the sides by same positive number The inequality reverses if it is multiplied or divide by a negative number a < b b > a a < b 1/a > 1/b x2 ≤ a2 x ≤ a and x ≥ -a Points to remember x = 0 is y-axis y = 0 is x-axis x = k is a line parallel to y-axis passing through (k, 0) of x-axis. y = k is a line parallel to x-axis passing through (0, k) of y-axis. Method to find Graphical Solution Draw lines corresponding to each equation treating it as equality. Find the feasible region: intersection of all the inequalities. LEVEL – I Solve 24x < 100 when x is a natural number. Solve the inequalities and draw the graph of the solution on number line: 3x – 2 < 2x + 1. Solve the following system of inequalities: 2x + y ≥ 8, x + 2y ≥ 10. the following system of inequalities graphically: x ≥ 3, y ≥ 2. the following system of inequalities graphically: x + y ≤ 9, y>x, x≥0. Find all of consecutive odd positive integers both of which are smaller than 10 such that there sum is more than 11. LEVEL – II the inequalities and draw the graph of the solution on number line: 5(2x – 7) – 3(2x + 3) ≤ 0. the following system of inequalities graphically: x + y ≤ 400, 2x + y ≤ 600.
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