11-20 Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤) instead of an equal sign.

Front

What does the solution of a system of inequalities represent?

Back

The solution of a system of inequalities represents all the points (x, y) that satisfy all inequalities in the system simultaneously.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, shade the region that satisfies the inequality (above the line for 'greater than' and below for 'less than').

Front

What is the difference between '≤' and '<'?

Back

'≤' means 'less than or equal to', while '<' means 'less than' only. The former includes the boundary line in the solution set, while the latter does not.

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to the specified number.

Front

If a point (x, y) is a solution to a system of inequalities, what can be said about its position relative to the boundary lines?

Back

The point (x, y) must lie in the shaded region of the graph, which represents the solution set of the inequalities.

Front

How can you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the x and y values into each inequality. If all inequalities are satisfied, the point is a solution.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the solution set from the non-solution set. It is included in the solution if the inequality is '≤' or '≥'.

Front

Write the system of inequalities for a scenario where a theater has 300 seats and needs to make at least $2000 from ticket sales.

Back

x + y ≤ 300 (total seats) and 7.5x + 5.5y ≥ 2000 (revenue requirement).

Front

What does it mean if a point is 'not a solution' to a system of inequalities?

Back

If a point is 'not a solution', it means that when substituted into the inequalities, at least one inequality is not satisfied.