Linear Inequalities in One Variable A linear inequality is an inequality that expresses a comparison between a linear expression and a constant . The...
A linear inequality is an inequality that expresses a comparison between a linear expression and a constant. The linear expression can be a constant multiplied by a variable, a sum of two or more linear expressions, or a subtraction of two linear expressions.
A linear inequality can have one of two forms:
Greater than/Less than: The inequality states that the value on the left side of the inequality is greater than or less than the value on the right side.
Greater than/Less than or equal to: The inequality states that the value on the left side of the inequality is greater than or equal to the value on the right side.
Solving a linear inequality involves isolating the variable on one side of the inequality using algebraic manipulations like addition, subtraction, multiplication, and division. Once the variable is isolated, we compare it to the constant on the right side of the inequality to determine the solution.
Examples:
x > 2 expresses the statement that x is greater than 2.
x ≤ 5 expresses the statement that x is less than or equal to 5.
3x ≥ 18 expresses the statement that 3x is greater than or equal to 18.
x + 4 ≤ 10 expresses the statement that x is greater than or equal to 10 - 4.
Linear inequalities play a crucial role in various mathematical fields, including mathematics, physics, economics, and finance. They are used to model real-world situations, solve problems, and make predictions