Inequalities - 3 Video Lecture | Quantitative Aptitude (Quant) - CAT

Ans. Inequalities in mathematics represent the relationship between two expressions or values that are not equal. They can be expressed using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Inequalities are used to compare the size or magnitude of different quantities.

Ans. To solve inequalities with variables on both sides, the first step is to simplify the expression by collecting like terms and combining constants. Then, isolate the variable on one side of the inequality by performing inverse operations (opposite operations) such as addition/subtraction or multiplication/division. Finally, check the solution by substituting the obtained value back into the original inequality to ensure its validity.

Ans. The basic rules for solving inequalities are similar to solving equations. However, there are some additional rules specific to inequalities. These rules include: - When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality sign must be reversed. - When adding or subtracting a positive or negative number from both sides of an inequality, the direction of the inequality sign remains the same. - When multiplying or dividing both sides of an inequality by a positive number, the direction of the inequality sign remains the same. - When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.

Ans. Graphing inequalities on a number line involves representing the solution set of the inequality visually. - For inequalities with < or > symbols (strict inequalities), use an open circle to represent the endpoint and draw an arrow in the direction of the solution. - For inequalities with ≤ or ≥ symbols (inclusive inequalities), use a closed circle to represent the endpoint and draw an arrow in the direction of the solution. - If there is a range of values that satisfy the inequality, shade the corresponding region on the number line.

Ans. The main difference between solving equations and solving inequalities is that equations find a specific value or set of values that make the equation true, while inequalities find a range of values that satisfy the inequality. In equations, the goal is to isolate the variable and determine its exact value. In inequalities, the goal is to determine the set of values that make the inequality true by considering the range of possible solutions.