Solving Inequalities

An inequality is a mathematical statement that compares two expressions using inequality symbols such as <, >, ≤, or ≥.

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

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

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

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

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

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

The graph should show an open circle at 2 and a line extending to the right.

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

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