Graphing and Solving Inequalities on Number Line

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

Front

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

Back

The symbol '>' 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

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

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 greater than or equal to 2.

Front

How do you represent the inequality k < 3 on a number line?

Back

Draw a number line, place an open circle at 3, and shade to the left to indicate all numbers less than 3.

Front

What does the graph of x < -4 look like on a number line?

Back

An open circle at -4 with shading to the left, indicating all numbers less than -4.

Front

How do you solve the inequality 5z - 2 - 2z < 13?

Back

Combine like terms to get 3z - 2 < 13, then add 2 to both sides to get 3z < 15, and finally divide by 3 to find z < 5.

Front

What does the graph of x ≥ -5 look like on a number line?

Back

A closed circle at -5 with shading to the right, indicating all numbers greater than or equal to -5.

Front

How do you solve the inequality 5(v + 3) - 10v > -10?

Back

Distribute to get 5v + 15 - 10v > -10, combine like terms to get -5v + 15 > -10, then subtract 15 from both sides to find -5v > -25, and divide by -5 to get v < 5.