Unit 2 review - 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 (such as <, >, ≤, or ≥). It represents a region of the coordinate plane.

Front

How do you write a linear inequality in standard form?

Back

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the values of the expression can be equal to or less than the specified value.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the values of the expression can be equal to or greater than the specified value.

Front

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

Back

To determine if a point (x, y) is a solution, substitute the x and y values 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 of a linear inequality is the set of all points (x, y) that satisfy the inequality, often represented as a shaded region on a graph.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (using < or >) does not include the boundary line, while a non-strict inequality (using ≤ or ≥) includes the boundary line.

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 appropriate region based on the inequality.

Front

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

Back

The boundary line represents the values where the inequality changes from true to false. Points on the line are included if the inequality is non-strict (≤ or ≥).

Front

How do you solve a system of linear inequalities?

Back

To solve a system of linear inequalities, graph each inequality on the same coordinate plane and identify the region where all shaded areas overlap. This overlapping region represents the solution set.