Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is any number greater than 3.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. For example, x < 5 means x is any number less than 5.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 2 means x is any number greater than or equal to 2.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 4 means x is any number less than or equal to 4.

Front

How do you graph the inequality y > 2x - 5?

Back

To graph y > 2x - 5, first graph the line y = 2x - 5 as a dashed line (since it's not inclusive), then shade above the line.

Front

How do you graph the inequality y ≤ -3x + 1?

Back

To graph y ≤ -3x + 1, first graph the line y = -3x + 1 as a solid line (since it's inclusive), then shade below the line.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true.

Front

How can you determine if a point is a solution to an 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, the point is a solution.

Front

What is the difference between '>' and '≥'?

Back

'>' means the value is strictly greater, while '≥' includes the value itself as part of the solution.