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Introduction to Linear Inequalities Video Lecture | Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

FAQs on Introduction to Linear Inequalities Video Lecture - Mathematics (Maths) for JEE Main & Advanced

1. What are linear inequalities?
Ans. Linear inequalities are mathematical expressions that compare two quantities using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). They define a range of possible values for a variable.
2. How do you graph a linear inequality?
Ans. To graph a linear inequality, first, graph the corresponding linear equation (the line). Then, depending on the inequality symbol, shade the region above or below the line. If the inequality includes an equal sign, the line should be solid; otherwise, it should be dashed.
3. How do you solve a system of linear inequalities?
Ans. To solve a system of linear inequalities, graph each inequality on the same coordinate plane. The solution is the overlapping region where all the shaded regions intersect. It represents the values that satisfy all the given inequalities simultaneously.
4. What is the difference between a linear equation and a linear inequality?
Ans. A linear equation is an equation that represents a straight line on a graph, where the two sides of the equation are equal. On the other hand, a linear inequality represents a range of values, where the two sides of the inequality are not equal. In linear inequalities, the solution can be a set of values rather than a single point.
5. How do you solve a linear inequality algebraically?
Ans. To solve a linear inequality algebraically, treat it as an equation until you reach a point where you need to determine the direction of the inequality. If you multiply or divide both sides of the inequality by a negative number, reverse the direction of the inequality. The solution is often expressed in interval notation or set notation.
209 videos|443 docs|143 tests

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