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 (e.g., <, >, ≤, ≥).

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

How do you determine if a point is a solution to the inequality x + y < 7?

Back

Substitute the x and y values of the point into the inequality. If the resulting statement is true, then the point is a solution.

Front

What is the significance of a dotted line in a 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

If a point lies in the shaded region of a graph of a linear inequality, what can be concluded?

Back

If a point lies in the shaded region, it is a solution to the inequality.

Front

What is the difference between 'sometimes' and 'no' when determining if a point is a solution?

Back

'Sometimes' implies that the point may be a solution under certain conditions, while 'no' means the point is definitely not a solution.

Front

What is the first step in solving a linear inequality?

Back

The first step is to isolate the variable on one side of the inequality.

Front

How can you check if a point is a solution to an inequality?

Back

Substitute the coordinates of the point into the inequality and see if the inequality holds true.

Front

What does the term 'solution set' refer to in the context of linear inequalities?

Back

The solution set is the collection of all points that satisfy the inequality.