Question 10

x = -1

To solve the equation 2(4x + 3) = 7x + 5, we simplify to find that x equals -1, demonstrating that this is the solution to the given equation.

A) -1

Option A is correct because substituting x = -1 back into the original equation confirms the equality: 2(4(-1) + 3) = 7(-1) + 5 simplifies to 2(-4 + 3) = -7 + 5, which further simplifies to 2(-1) = -2, validating that both sides equal -2.

B) 1

Option B is incorrect as substituting x = 1 into the original equation results in 2(4(1) + 3) = 7(1) + 5, which simplifies to 2(4 + 3) = 7 + 5. This gives 2(7) = 12, or 14 = 12, which is not true.

C) 11

Option C is also incorrect. If we substitute x = 11, the left side becomes 2(4(11) + 3) = 2(44 + 3) = 2(47) = 94, while the right side becomes 7(11) + 5 = 77 + 5 = 82. Since 94 does not equal 82, this option does not satisfy the equation.

D) 2

Option D is incorrect as well. When substituting x = 2, the left side becomes 2(4(2) + 3) = 2(8 + 3) = 2(11) = 22, and the right side becomes 7(2) + 5 = 14 + 5 = 19. Since 22 does not equal 19, this option also fails to solve the equation.

Conclusion

In summary, the only correct solution to the equation 2(4x + 3) = 7x + 5 is x = -1, as verified by substitution. All other options do not satisfy the equality when plugged back into the original equation, demonstrating that they are incorrect choices.