Solve 2x + 1 greater than -3 and 3x - 4 less than or equal to 5, in interval notation.

1. Take the first inequality on its own: 2x plus 1 greater than negative 3. 2. Subtract 1 to get 2x greater than negative 4, then divide by 2 to get x greater than negative 2. 3. Now take the second: 3x minus 4 less than or equal to 5. 4. Add 4 to get 3x less than or equal to 9, then divide by 3 to get x less than or equal to 3. 5. The joining word is and, so keep only the numbers satisfying both. 6. That is every number above negative 2 and up to 3 inclusive. 7. The strict sign at negative 2 gives a parenthesis, and the inclusive sign at 3 gives a bracket. 8. The interval [-2, 3) swaps the two endpoint marks around. 9. The interval (-2, 3) drops 3 even though the second inequality allows it. 10. The interval [-2, 3] adds negative 2 even though the first inequality excludes it. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.6 Solve Compound Inequalities_