Course 2 - Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the region that satisfies the inequality.

Front

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

Back

'>' means 'greater than'. For example, x > 5 means x is any number greater than 5.

Front

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

Back

'<'' means 'less than'. For example, x < 3 means x is any number less than 3.

Front

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

Back

'≥' means 'greater than or equal to'. For example, x ≥ 4 means x is any number greater than or equal to 4.

Front

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

Back

'≤' means 'less than or equal to'. For example, x ≤ 2 means x is any number less than or equal to 2.

Front

How do you solve the inequality 2x + 3 < 7?

Back

Subtract 3 from both sides: 2x < 4. Then divide by 2: x < 2.

Front

What is the solution set for the inequality x > 5?

Back

The solution set is all real numbers greater than 5, often written in interval notation as (5, ∞).

Front

How do you represent the solution of an inequality on a number line?

Back

Draw a number line, place a dot at the boundary number, and use an open circle for < or > and a closed circle for ≤ or ≥. Shade the direction of the solution.

Front

What is the difference between a solid line and a dashed line when graphing inequalities?

Back

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