Solve and Graph 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, or not equal to the other.

Front

What does the symbol '<' represent in inequalities?

Back

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

Front

What does the symbol '>' represent in inequalities?

Back

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

Front

How do you solve the inequality -3x - 4 < 5?

Back

Add 4 to both sides: -3x < 9. Then divide by -3 (remember to flip the inequality): x > -3.

Front

What is the solution to the inequality 0.5(x - 8) < 2?

Back

Multiply both sides by 2: x - 8 < 4. Then add 8: x < 12.

Front

When graphing the inequality x < 6, what type of circle is used?

Back

An open circle is used to indicate that 6 is not included in the solution.

Front

What does a closed dot represent when graphing inequalities?

Back

A closed dot indicates that the number is included in the solution, as in x ≤ 5.

Front

How do you graph the inequality x > 4?

Back

Draw a number line, place an open circle at 4, and shade to the right to indicate all numbers greater than 4.

Front

What is the difference between '≤' and '<'?

Back

'≤' means 'less than or equal to', while '<' means 'less than' only.

Front

What is the solution set for the inequality x + 3 > 7?

Back

Subtract 3 from both sides: x > 4.