Solve the equation 2(4x + 3) = 7x + 5 for x. Which of the following is correct?

Rationale

The solution to the equation 2(4x + 3) = 7x + 5 is x = -1.

By distributing on the left side of the equation, we get 8x + 6 = 7x + 5. Subtracting 7x from both sides, we get x + 6 = 5. Subtracting 6 from both sides of this equation gives us the solution x = -1.

A (-1) CORRECT

This is the correct answer. By simplifying the given equation, we arrive at x = -1.

B (1) YOUR ANSWER

This is incorrect. Substituting x = 1 into the original equation gives 2(4*1 + 3) = 7*1 + 5, which simplifies to 14 = 12, a false statement.

C (11) YOUR ANSWER

This is incorrect. Substituting x = 11 into the original equation gives 2(4*11 + 3) = 7*11 + 5, which simplifies to 94 = 82, a false statement.

D (2) YOUR ANSWER

This is incorrect. Substituting x = 2 into the original equation gives 2(4*2 + 3) = 7*2 + 5, which simplifies to 22 = 19, a false statement.

Conclusion

The correct solution to the equation 2(4x + 3) = 7x + 5 is x = -1. The other choices (x = 1, x = 11, and x = 2) do not satisfy the given equation, making them incorrect answers. The process of algebraic simplification and substitution can be used to verify the correct answer and eliminate the incorrect ones.

Solve the equation 2(4x + 3) = 7x + 5 for x. Which of the following is correct?

The solution to the equation 2(4x + 3) = 7x + 5 is x = -1.

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