Linear Inequation — Important Questions

x = 3, x = 2, x = 1, x = 0

-2x + 6 ≥ 0 Subtract 6: -2x ≥ -6 Divide by -2 (reverse inequality): x ≤ 3 So x = 3, 2, 1, 0 are correct, but x = 4 is not since 4 > 3.

-2 < x ≤ 5

The phrase 'greater than -2' means x > -2 (not equal to -2) The phrase 'less than or equal to 5' means x ≤ 5 Combining: -2 < x ≤ 5

x < -4

-3x > 12 Divide both sides by -3 (reverse the inequality sign): x < -4 When dividing by a negative number, we must reverse the inequality sign.

A filled circle at 3 with arrow pointing right, A closed interval starting at 3, A thick line from 3 extending to the right

x ≥ 3 means x is greater than or equal to 3. On a number line: - Use a filled/closed circle at 3 (because x = 3 is included) - Draw an arrow or thick line extending to the right (for x > 3)