Retake PracticeSystems of Linear Inequalities Practical Problems

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 (such as <, >, ≤, or ≥). It represents a region of solutions on a graph.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side of the inequality is either greater than or equal to the value on the right side.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

How do you represent a situation where a total must be at least a certain number using inequalities?

Back

You use the '≥' symbol. For example, if a total must be at least 200, you would write the inequality as total ≥ 200.

Front

What is the significance of the solution set of a linear inequality?

Back

The solution set of a linear inequality represents all the possible values that satisfy the inequality. It can be graphed as a shaded region on a coordinate plane.

Front

How do you graph a linear inequality?

Back

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

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

Front

What does it mean if a linear inequality has no solution?

Back

If a linear inequality has no solution, it means that there are no values that can satisfy the inequality. This often occurs when the lines representing the inequalities are parallel and do not intersect.

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

Front

What is a feasible region in the context of linear inequalities?

Back

A feasible region is the area on a graph where all the constraints (linear inequalities) overlap. It represents all possible solutions that satisfy all inequalities.