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 (>, <, ≥, ≤).

Front

What does the shaded area represent when graphing linear inequalities?

Back

The shaded area represents all the solutions to the inequality.

Front

What type of line is used to represent 'greater than' or 'less than' in a graph?

Back

A dashed or dotted line is used to represent 'greater than' (>) or 'less than' (<) because points on the line are not included in the solution set.

Front

What type of line is used to represent 'greater than or equal to' or 'less than or equal to'?

Back

A solid line is used to represent 'greater than or equal to' (≥) or 'less than or equal to' (≤) because points on the line are included in the solution set.

Front

If the inequality is x < 3, what is the correct graph representation?

Back

The graph should have a dashed line at x = 3 and shade to the left.

Front

If the inequality is y ≥ 2x + 1, how should the line be drawn?

Back

The line should be solid because the inequality includes 'greater than or equal to'.

Front

What does it mean if a point lies in the shaded area of a graph of a linear inequality?

Back

It means that the point is a solution to the inequality.

Front

How do you determine which side of the line to shade when graphing a linear inequality?

Back

Choose a test point not on the line (usually (0,0) if it's not on the line) and substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

Front

What is the solution set of the inequality 2x + 3 < 7?

Back

The solution set is x < 2.

Front

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

Back

A linear equation shows equality (e.g., y = 2x + 1), while a linear inequality shows a relationship of inequality (e.g., y < 2x + 1).