Solving and Graphing 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, greater than or equal to, or less than or equal to 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 less than or equal to the value on the right.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Front

How do you solve the inequality -24 + k ≤ 10?

Back

To solve -24 + k ≤ 10, add 24 to both sides: k ≤ 34.

Front

How do you solve the inequality 10 ≥ x - 3?

Back

To solve 10 ≥ x - 3, add 3 to both sides: x ≤ 13.

Front

How do you solve the inequality 2x - 3 ≤ 3?

Back

To solve 2x - 3 ≤ 3, add 3 to both sides and then divide by 2: x ≤ 3.

Front

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

Back

Combine like terms: 3z - 2 < 13. Then add 2 to both sides and divide by 3: z < 5.

Front

What does the inequality x < 2 represent on a number line?

Back

It represents all values of x that are less than 2, shown with an open circle at 2 and a line extending to the left.

Front

What is the solution set for the inequality x ≥ 3?

Back

The solution set includes all values of x that are greater than or equal to 3, represented on a number line with a closed circle at 3 and a line extending to the right.

Front

What is the difference between 'strict' and 'non-strict' inequalities?

Back

Strict inequalities (<, >) do not include the boundary point, while non-strict inequalities (≤, ≥) do include the boundary point.