Question

Solve the inequality using the properties of inequality
3(2x+1) - 2(x-3) > 24

Answer 1

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:

1. Distribute the multiplication over addition for both terms: 3(2x+1) becomes 6x + 3, and -2(x-3) becomes -2x + 6.
2. Combine like terms: 6x + 3 - 2x + 6 simplifies to 4x + 9.
3. Subtract 9 from both sides of the inequality 4x + 9 > 24, giving us 4x > 15.
4. Divide both sides by 4 to isolate x, which results in x > 15/4.

The answer is x > 3.75.