Introduction: This is a straightforward algebra topic. The most important rule to remember is to flip the inequality sign whenever you multiply or divide both sides by a negative number.

The "S Pass" Foundation (නියත S එකකට)

• Prompt 1 (Solve): Solve the inequality x+5>8.

• Prompt 2 (Solve): Solve the inequality 3y≤12.

• Prompt 3 (Solve): Solve the inequality 2x−1<7.

• Prompt 4 (Representation): Represent the integer solutions of x≥−2 on a number line.

• Prompt 5 (The Rule): What happens to the inequality sign when you divide both sides by -3?

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Solve): Solve the inequality 5−3x>11.

• Prompt 2 (Solve): Solve: 4x+7≤2x+15.

• Prompt 3 (Representation): Represent the solution set of 2x−5<x−1 on a number line.

• Prompt 4 (Problem Solve): Find the largest integer that satisfies the inequality 3x−4≤8.

• Prompt 5 (Word Problem): The sum of two consecutive integers is less than 45. Find the largest possible values for the integers.

Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Solve): Solve the inequality 32x−1​>x+1.

• Prompt 2 (Problem Solve): The perimeter of an equilateral triangle must be greater than the perimeter of a square. If the side of the triangle is (x+4) cm and the side of the square is x cm, form an inequality and find the smallest integer value of x.

• Prompt 3 (Compound Inequality): Find the integer solutions for −3≤2x−1<5.

• Prompt 4 (Justify): A student solves −5x≥20 and gets the answer x≥−4. Is this correct? Explain the mistake and provide the correct solution.

• Prompt 5 (Word Problem): A person has Rs. 2000 to spend on books and pens. A book costs Rs. 250 and a pen costs Rs. 40. If they buy 5 books, what is the maximum number of pens they can buy?

Securing the "A" Distinction (A සාමාර්ථය තහවුරු කරගන්න)

• Prompt 1 (Challenge): Find the range of values of x for which the area of a rectangle with sides (x−3) and (x+2) is positive but less than 14.

• Prompt 2 (Graphical): Sketch the graphs of y=x+1 and y=7−x. Use your sketch to find the range of x-values for which x+1<7−x.

• Prompt 3 (Synthesis): The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. If a triangle has sides of length 5 cm, 12 cm, and (2x−1) cm, form and solve inequalities to find the possible range of values for x.

• Prompt 4 (Quadratic Inequality): Find the set of values of x for which x2−5x+4>0. (Hint: Factorise and consider the graph or a number line).

Prompt 5 (Problem Solve): A school needs to hire buses for 300 students. Small buses can carry 25 students and cost Rs. 8000. Large buses can carry 40 students and cost Rs. 10000. They can hire at most 10 buses in total. Formulate inequalities and find the combination of buses that minimizes the cost.