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

Front

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

Back

The symbol '<' means 'less than'. For example, x < 3 means x is less than 3.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 4 means x is greater than or equal to 4.

Front

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

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 2 means x is less than or equal to 2.

Front

How do you solve the inequality 3(x - 2) < 2(x + 9)?

Back

First, distribute: 3x - 6 < 2x + 18. Then, subtract 2x from both sides: x - 6 < 18. Finally, add 6 to both sides: x < 24.

Front

When do you flip the inequality symbol?

Back

You flip the inequality symbol when you multiply or divide both sides of the inequality by a negative number.

Front

How can you represent a range of values in an inequality?

Back

You can represent a range of values using compound inequalities, such as 2 ≤ x ≤ 8, which means x is between 2 and 8, inclusive.

Front

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

Back

The graph of x ≥ -5 includes a closed dot at -5 and a line extending to the right, indicating all numbers greater than or equal to -5.

Front

What is the solution to the inequality 6 > x?

Back

The solution to the inequality 6 > x is x < 6.