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?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

How do you solve the inequality -3x + 2 ≤ 22?

Back

Subtract 2 from both sides: -3x ≤ 20. Then divide by -3 (flip the sign): x ≥ -20/3.

Front

What is the solution to the inequality 2x + 3 < 7?

Back

Subtract 3 from both sides: 2x < 4. Then divide by 2: x < 2.

Front

What does it mean to 'flip the sign' when solving inequalities?

Back

Flipping the sign means changing the direction of the inequality symbol when multiplying or dividing by a negative number.

Front

What is the solution to the inequality 6x - 4 ≥ 26?

Back

Add 4 to both sides: 6x ≥ 30. Then divide by 6: x ≥ 5.

Front

Which graph represents the inequality x > 2?

Back

The graph should show an open circle at 2 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 endpoint, while non-strict inequalities (≤, ≥) do include the endpoint.

Front

How do you graph the inequality 2x + 3 < 7?

Back

First, solve for x: 2x < 4, x < 2. Then graph with an open circle at 2 and shade to the left.