Question

Solve the equation using the properties of equality.

3.) 3(2x+1) - 2(x-3) = 24
A. x = 3
B. x = 5
C. x = 6
D. x = 7

Answer 1

The solution for the equation 3(2x+1) - 2(x-3) = 24 is x = 3.75 by distributing multiplication across parentheses, combining like terms, and isolating x. However, this solution does not match any of the provided answer choices.

Step-by-step explanation:

To solve the equation 3(2x+1) - 2(x-3) = 24 using the properties of equality, we need to follow these steps:

1. Distribute the numbers outside the parentheses: 6x + 3 - 2x + 6 = 24.
2. Combine like terms: (6x - 2x) + (3 + 6) = 24, which simplifies to 4x + 9 = 24.
3. Subtract 9 from both sides to isolate the term with x: 4x = 15.
4. Finally, divide both sides by 4 to solve for x: x = 15 / 4, which simplifies to x = 3.75.

None of the options given (A. x = 3, B. x = 5, C. x = 6, D. x = 7) match the solution x = 3.75. Therefore, there might be an error in the options provided or in the initial problem statement.