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Inequalities - 4 Video Lecture | Quantitative Aptitude (Quant) - CAT

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FAQs on Inequalities - 4 Video Lecture - Quantitative Aptitude (Quant) - CAT

1. What are inequalities in mathematics?
Ans. Inequalities in mathematics represent a relationship between two values that are not equal. It compares the quantities using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
2. How do you solve inequalities?
Ans. To solve inequalities, follow these steps: 1. Treat the inequality sign as an equal sign and solve the equation. 2. Determine the direction of the inequality based on the sign. If it is "<" or ">", use an open circle on the number line. If it is "<=" or ">=", use a closed circle. 3. Shade the region on the number line that satisfies the inequality. 4. Write the solution using interval notation or set-builder notation.
3. What is the difference between a solution and an inequality?
Ans. An inequality is a mathematical statement that compares two values, while a solution refers to the values that satisfy the inequality. In other words, a solution is a specific value or set of values that make the inequality true when substituted into it.
4. How do you graph inequalities on a coordinate plane?
Ans. To graph inequalities on a coordinate plane, follow these steps: 1. Treat the inequality as an equation and graph the corresponding line. 2. Determine whether the line should be solid or dashed based on the inequality sign. If it is "<" or ">", use a dashed line. If it is "<=" or ">=", use a solid line. 3. Choose a test point not on the line and substitute its coordinates into the inequality. 4. Shade the region of the graph where the test point satisfies the inequality.
5. What are the common mistakes to avoid when solving inequalities?
Ans. Some common mistakes to avoid when solving inequalities include: - Forgetting to reverse the inequality sign when multiplying or dividing by a negative number. - Incorrectly distributing a negative sign when multiplying or dividing by an expression. - Not considering the case when the variable is in the denominator and could lead to division by zero. - Forgetting to change the direction of the inequality when multiplying or dividing by a negative number.
181 videos|146 docs|111 tests

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