Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (e.g., <, >, ≤, ≥) to show that one expression is larger or smaller than the other.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be either less than or equal to the value on the right.

Front

What does the symbol '>' mean?

Back

The symbol '>' means 'greater than'. It indicates that the value on the left is strictly larger than the value on the right.

Front

When solving the inequality 4x - 10 ≤ 22, what is the first step?

Back

The first step is to isolate the variable term by adding 10 to both sides of the inequality.

Front

What is the solution to the inequality 4x - 10 ≤ 22?

Back

The solution is x ≤ 8.

Front

When graphing the inequality x > 5, what type of circle is used?

Back

An open circle is used when graphing x > 5, indicating that 5 is not included in the solution.

Front

What happens to the inequality sign when multiplying or dividing by a negative number?

Back

When multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be flipped.

Front

Solve the inequality -3x + 2 ≤ 22. Do you flip the sign?

Back

Yes, you flip the sign when isolating x, resulting in x ≥ -7.

Front

What is the solution to the inequality -2x + 2 > 3x - 8?

Back

The solution is x < 2.

Front

What does a closed circle represent when graphing inequalities?

Back

A closed circle represents that the endpoint is included in the solution set, used for ≤ or ≥.