Writing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality 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 can be any number 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 can be any number greater than or equal to 2.

Front

How do you graph the inequality x < 3?

Back

To graph x < 3, draw a number line, place an open circle at 3, and shade to the left to indicate all numbers less than 3.

Front

How do you graph the inequality x ≥ -1?

Back

To graph x ≥ -1, draw a number line, place a closed circle at -1, and shade to the right to indicate all numbers greater than or equal to -1.

Front

What is the difference between an open circle and a closed circle on a graph?

Back

An open circle indicates that the number is not included (e.g., x < 3), while a closed circle indicates that the number is included (e.g., x ≤ 3).

Front

How would you write the inequality for 'You have less than $50 to spend'?

Back

The inequality is written as x < 50, where x represents the amount of money you have.

Front

What is the solution set for the inequality x < -2?

Back

The solution set for x < -2 includes all numbers less than -2, represented on a number line with an open circle at -2 and shading to the left.