Two-Variable Inequalities

Front

What is a two-variable inequality?

Back

A two-variable inequality is a mathematical statement that compares two expressions involving two variables, typically written in the form of 'ax + by <, >, ≤, or ≥ c'.

Front

What does the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than'. It 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 inequalities?

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

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. It 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 inequalities?

Back

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

Front

How do you graph a two-variable inequality?

Back

To graph a two-variable inequality, first graph the corresponding equation as a line. Then, use a dashed line for '<' or '>' and a solid line for '≤' or '≥'. Finally, shade the appropriate region based on the inequality.

Front

What is the solution set of an inequality?

Back

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

Front

How can you determine if a point is in the solution set of an inequality?

Back

To determine if a point is in the solution set, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is in the solution set.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities ('<' and '>') do not include the boundary line, while non-strict inequalities ('≤' and '≥') include the boundary line.

Front

What is the significance of the boundary line in a two-variable inequality?

Back

The boundary line represents the values where the inequality changes from true to false. It divides the graph into regions that satisfy or do not satisfy the inequality.