Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

Front

What does the symbol ≤ represent in a linear inequality?

Back

The symbol ≤ means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol ≥ represent in a linear inequality?

Back

The symbol ≥ means 'greater than or equal to', indicating that the value on the left can be greater than or equal to the value on the right.

Front

How do you graph a linear inequality with a solid line?

Back

A solid line is used when the inequality includes ≤ or ≥, indicating that points on the line are included in the solution set.

Front

How do you graph a linear inequality with a dashed line?

Back

A dashed line is used when the inequality includes < or >, indicating that points on the line are not included in the solution set.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is typically written as Ax + By ≤ C or Ax + By ≥ C, where A, B, and C are constants.

Front

How do you convert a word problem into a linear inequality?

Back

Identify the quantities involved, determine the relationship between them, and express it using inequality symbols based on the context.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, often represented as a shaded region on a graph.

Front

What does the inequality x < -1 represent on a number line?

Back

The inequality x < -1 represents all numbers to the left of -1 on a number line, not including -1 itself.

Front

How do you determine if a point is a solution to a linear inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.