Solve the inequality: 2x − 5 > 7

Solve inequalities like equations, but reverse the inequality sign when multiplying or dividing by a negative. Step 1: add 5: 2x > 12. Step 2: divide by 2 (positive, so don't flip): x > 6. Verify: try x = 7: 2(7) − 5 = 9 > 7 ✓; try x = 5: 2(5) − 5 = 5, not > 7 ✗. Inequality symbols: (1) > greater than (strict); (2) < less than (strict); (3) ≥ greater than or equal; (4) ≤ less than or equal. Number line representation: open circle for strict (>, <); closed circle for ≥, ≤; arrow indicates direction. Critical rule: multiplying or dividing both sides by a negative REVERSES the inequality. Example: −2x > 10 becomes x < −5 (divide both sides by −2, flip the >). Adding/subtracting and multiplying/dividing by positives does NOT flip. Compound inequalities: 'and' (intersection, both must hold) vs 'or' (union, either holds). Example: x > 2 AND x < 5 means 2 < x < 5.