Solutions to 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 it mean for a point to be a solution to a linear inequality?

Back

A point is a solution to a linear inequality if it satisfies the inequality when the coordinates of the point are substituted into the inequality.

Front

What is the significance of a dotted line in the graph of a linear inequality?

Back

A dotted line indicates that points on the line are not included in the solution set of the inequality.

Front

What does a solid line represent in the graph of a linear inequality?

Back

A solid line indicates that points on the line are included in the solution set of the inequality.

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, then the point is a solution.

Front

What is the solution set of a linear inequality?

Back

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

Front

What does the shaded region in the graph of a linear inequality represent?

Back

The shaded region represents all the solutions to the inequality.

Front

How can you tell if a point is in the shaded region of a graph?

Back

A point is in the shaded region if it satisfies the inequality represented by the graph.

Front

What is the difference between 'y > mx + b' and 'y < mx + b'?

Back

'y > mx + b' represents the region above the line, while 'y < mx + b' represents the region below the line.

Front

What does the inequality 'x + y < 7' represent graphically?

Back

It represents all the points below the line x + y = 7.