Final answer:
To solve the inequality 3(2x+1) - 2(x-3) > 24, distribute the terms, combine like terms, subtract 9 from both sides, and then divide by 4 to isolate x, resulting in x > 3.75.
Step-by-step explanation:
To solve the inequality using the properties of inequality, we'll work step-by-step:
- Distribute the multiplication over addition for both terms: 3(2x+1) becomes 6x + 3, and -2(x-3) becomes -2x + 6.
- Combine like terms: 6x + 3 - 2x + 6 simplifies to 4x + 9.
- Subtract 9 from both sides of the inequality 4x + 9 > 24, giving us 4x > 15.
- Divide both sides by 4 to isolate x, which results in x > 15/4.
The answer is x > 3.75.