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Questions and Answers
What is the highest power of the variable in a linear inequality?
How many variables are involved in a linear inequality in two variables?
Which method is used to solve a system of linear inequalities algebraically?
What happens to the sign of an inequality when both sides are multiplied or divided by a negative number?
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Which property states that if a > b and b > c, then a > c?
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How are linear inequalities represented graphically?
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Why is it important to multiply or divide both sides of an inequality by a positive number?
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Study Notes
Linear Inequations
Definition
- A linear inequation is an inequality in which the highest power of the variable(s) is 1.
- It can be represented as ax + by >, <, ≥, ≤ cx + dy, where a, b, c, and d are constants.
Types of Linear Inequations
- Simple Linear Inequation: Involves only one variable.
- Example: 2x - 3 > 5
- Linear Inequation in Two Variables: Involves two variables.
- Example: 2x + 3y > 7
Graphical Representation
- Linear inequations can be represented on a number line or a graph.
- The solution region is the section of the number line or graph that satisfies the inequation.
Methods of Solving Linear Inequations
- Substitution Method
- Graphical Method
- Algebraic Method
Properties of Linear Inequations
- Transitive Property: If a > b and b > c, then a > c.
- Addition Property: If a > b, then a + c > b + c.
- Multiplication Property: If a > b and c > 0, then ac > bc.
Solving Systems of Linear Inequations
- Graphical Method: Shade the common region of the two inequations.
- Algebraic Method: Solve the system of inequations by substitution or elimination method.
Important Points
- Always multiply or divide both sides of the inequation by a positive number to avoid changing the sign of the inequation.
- Always reverse the sign of the inequation when multiplying or dividing both sides by a negative number.
Linear Inequations
Definition
- Linear inequations have the highest power of the variable(s) as 1.
- Can be represented as ax + by >, <, ≥, or ≤.
- Example: 2x + 3y > 7 is a linear inequation in two variables.
Graphical Representation
- Linear inequations can be represented on a number line or graph.
- The solution region is the section of the number line or graph that satisfies the inequation.
Methods of Solving Linear Inequations
- Substitution Method: Substitute the value of one variable into the other equation.
- Graphical Method: Represent the inequations on a graph and find the solution region.
- Algebraic Method: Solve the inequations using algebraic operations.
Properties of Linear Inequations
- Transitive Property: If a > b and b > c, then a > c.
- Addition Property: If a > b, then a + c > b + c.
- Multiplication Property: If a > b and c > 0, then ac > bc.
Solving Systems of Linear Inequations
- Graphical Method: Shade the common region of the two inequations.
- Algebraic Method: Solve the system of inequations by substitution or elimination method.
Important Points
- Always multiply or divide both sides of the inequation by a positive number to avoid changing the sign.
- Reverse the sign of the inequation when multiplying or dividing both sides by a negative number.
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Description
Learn about linear inequations, their definition, types, and graphical representation. Understand simple linear inequations and linear inequations in two variables.
