# Grade B Represent Linear Inequalities Represent the solution

Grade B Represent Linear Inequalities Represent the solution of a linear inequality in two variables on a number line, using set notation and on a graph If you have any questions regarding these resources or come across any errors, please contact [email protected]. org. uk

Key Vocabulary Inequality Solution Element Dataset Set Notation Variable Integers Constraints

How to shade unwanted regions If we are given the line x+2 y=2 then we can represent this on a graph as a straight line. Every point along the line will be where x+2 y=2 If we wanted to satisfy the inequality x+2 y≥ 2 then this would be EVERYTHING above the line. Therefore we would shade the UNWANTED region – BELOW the line. x+2 y≥ 2

How to use set notation A set is a collection of objects which are enclosed by brackets. Take for example this graph, the WANTED region has been left unshaded. CURLY BRACKETS FOR SET NOTATION The dataset would be: x x x x {(0, 0), (0, 1) , (0, 2), (0, 3), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1), (4, 0), (5, 0)}

How to use set notation However do all these elements in the dataset satisfy the three inequalities? {(0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1), (4, 0), (5, 0)} As the inequalities are dotted lines – we cannot include any solutions on the inequalities. x x We are therefore left with the solution set: x x { (1, 1), (1, 2), (2, 1), (3, 1)} x x x

How to use set notation The dataset has the following integer solutions, how can we find the three inequalities which satisfy this? {(1, 0), (2, 0), (3, 0)} x x x

How to use set notation The dataset has the following integer solutions, how can we find the three inequalities which satisfy this? {(1, 0), (2, 0), (3, 0)} Step 1: Draw inequalities which enclose the solutions Step 2: Find the equations of the lines to make the solution set true x x x Inequalities to make solution set true are x>0, y≥ 0 and y≤-⅓+1

Now you try. . . 1. a) Represent the inequalities y≥ 2 x, x>-1 and -x+4≥y by shading the unwanted regions. b) Using set notation determine the solution set

Now you try. . . 1. a) Represent the inequalities y≥ 2 x, x>-1 and -x+4≥y by shading the unwanted regions. b) Using set notation determine the solution set a) b) {(0, 0), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3)}

Now you try. . . 2. Three inequalities have been plotted below. Is the solution set correct? {(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (-1, 0), (-1, 1), (-1, 2), (-1, 3), (-2, 1), (-2, 2)}

Now you try. . . 2. Three inequalities have been plotted below. Is the solution set correct? {(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (-1, 0), (-1, 1), (-1, 2), (-1, 3), (-2, 1), (-2, 2)} Red is not in solution set

Problem Solving and Reasoning Jenny and Tom are selling cookies. They have 6 boxes altogether? They must sell at least 1 box each. What different combinations could they each sell?

Problem Solving and Reasoning Jenny and Tom are selling cookies. They have 6 boxes altogether? They must sell at least 1 box each. What different combinations could they each sell? Step 1: Form the inequalities Step 2: Draw inequalities and shade unwanted regions T+j<6 t>1 j>1

Problem Solving and Reasoning Jenny and Tom are selling cookies. They have 6 boxes altogether? They must sell at least 1 box each. What different combinations could they each sell? Step 3: Identify the combinations in the region {(2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (4, 1)} Make sure you put the combinations in the correct context of the question!

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