Writing and Graphing Linear Inequalities and Systems

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 (>, <, ≥, ≤).

Front

How do you write an inequality for a situation?

Back

Identify the variables, determine the relationship between them, and express it using an inequality symbol.

Front

What does the symbol '≥' indicate in an inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to a certain number.

Front

What does the symbol '≤' indicate in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value can be either less than or equal to a certain number.

Front

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

Back

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

Front

What is the significance of a solid line when graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (for '≥' or '≤' inequalities).

Front

What is the significance of a dashed line when graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set (for '>' or '<' inequalities).

Front

Write the inequality for earning at least $85 with babysitting and tutoring jobs.

Back

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation. 2. Use a solid or dashed line based on the inequality. 3. Shade the appropriate region that satisfies the inequality.

Front

What is a solution set in the context of inequalities?

Back

The solution set is the set of all points (x, y) that satisfy the inequality.