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 such as <, >, ≤, or ≥.

Front

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

Back

The symbol '>' means 'greater than' and indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

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

Back

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

Front

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

Back

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

Front

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

Back

The symbol '≤' means 'less than or equal to' and indicates that the value on the left side is either smaller than or equal to the value on the right side.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all ordered pairs (x, y) that satisfy the inequality.

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 dotted line (for < or >), then shade the region that represents the solution set.

Front

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

Back

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

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, then 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.