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Introduction to Linear Inequations

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Questions and Answers

What is the meaning of the inequality sign $\geq$ ?

Greater than or equal to

What is a linear inequality?

An inequality that involves a linear expression.

What is the difference between a linear equation and a linear inequality?

A linear equation represents equality, while a linear inequality represents an unequal relationship.

What is the purpose of solving a linear inequality?

To find the values of the variable that satisfy the inequality. Signup and view all the answers

The solution to a linear inequality is always a single value.

False (B) Signup and view all the answers

What are the two basic rules for solving a linear inequality?

Rule 1: Adding or subtracting the same term on both sides of the inequality does not change the solution. Rule 2: Multiplying or dividing both sides of the inequality by the same positive number does not change the solution. However, multiplying or dividing by a negative number requires flipping the inequality sign. Signup and view all the answers

Study Notes

Introduction to Linear Inequations

Linear inequation: A statement that compares two expressions using inequality symbols (>, <, ≥, ≤).
Variables: Quantities that can take on different numerical values.
Conditions: Possible relations between quantities (x > y, x ≥ y, x < y, x ≤ y).
Examples: x < 8, x ≥ 5, x + 4 ≤ 3.

Linear Inequations in One Variable

Real numbers: Numbers that can be represented on a number line, including integers, fractions, and decimals.
Forms: ax + b > c, ax + b < c, ax + b ≥ c, ax + b ≤ c.
Interpretation: Example ax + b > c means 'ax + b is greater than c'.
Signs of inequality: >, <, ≥, ≤.

Solving Linear Inequations Algebraically

Solving: Finding the variable values satisfying the inequality.
Rule 1: Transposing a positive term changes its sign to negative when moving to the other side of the inequality. (e.g., 2x + 3 > 7 becomes 2x > 7 - 3)
Rule 2: Transposing a negative term changes its sign to positive when moving to the other side of the inequality. (e.g., 2x – 3 > 7 becomes 2x > 7 + 3)

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Description

This quiz covers the fundamentals of linear inequations, including definitions, types, and rules for solving them algebraically. Participants will explore the properties of inequations in one variable and practice interpreting different forms of inequalities.