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