Linear Inequalities and Systems of 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 (>, <, ≥, ≤).

Front

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

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

What does the symbol '<' indicate in a linear inequality?

Back

The symbol '<' indicates that the value on the left is less than the value on the right.

Front

How do you determine if a line is solid or dashed in a graph of an inequality?

Back

A solid line indicates 'greater than or equal to' (≥) or 'less than or equal to' (≤), while a dashed line indicates 'greater than' (>) or 'less than' (<).

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.

Front

How do you graph the inequality y < 2x + 3?

Back

Graph the line y = 2x + 3 as a dashed line and shade below the line.

Front

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

Back

If a point lies on the boundary line of an inequality, it is included in the solution set if the line is solid (≥ or ≤) and not included if the line is dashed (> or <).

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more inequalities with the same variables.

Front

How do you find the solution to a system of linear inequalities?

Back

The solution to a system of linear inequalities is the region where the shaded areas of all inequalities overlap.

Front

What does the inequality y ≥ -x - 1 represent graphically?

Back

It represents a region above and including the line y = -x - 1.