Linear Inequalities Test pt 3

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 symbol '≤' mean in a linear inequality?

Back

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

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates 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?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). Then shade the region that satisfies the inequality.

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 make the inequality true, represented graphically as a shaded region on the coordinate plane.

Front

What is the difference between '>' and '≥'?

Back

The symbol '>' means 'greater than' and does not include the boundary line, while '≥' means 'greater than or equal to' and includes the boundary line.

Front

What is the purpose of solving a system of linear inequalities?

Back

The purpose is to find the set of values that satisfy all inequalities in the system simultaneously, represented as a common shaded region on a graph.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line of a linear inequality, it satisfies the equation of the line, and whether it is included in the solution set depends on the inequality symbol used.

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more linear inequalities that are considered together, and the solution is the intersection of the solution sets of each inequality.