Question 2

x = -54/7

To solve the equation ½ x + 9 = -2/3 x, we can rearrange the terms and isolate x. This leads to the solution of x = -54/7, confirming that this option is correct.

A) x = -9/7

This option is incorrect because when substituting x = -9/7 back into the original equation, the left-hand side does not equal the right-hand side. Therefore, it does not satisfy the equation.

B) x = -54/7

This is the correct option. When substituted back into the original equation, the left-hand side, ½(-54/7) + 9, simplifies to -27/7 + 63/7, which equals 36/7. The right-hand side, -2/3(-54/7), also simplifies to 36/7, confirming that both sides are equal.

C) x = -6

This option is also incorrect. Substituting x = -6 into the original equation results in ½(-6) + 9, which equals 6, while the right-hand side becomes -2/3(-6), equaling 4. The two sides do not match, disqualifying this option.

D) x = -54

This option is incorrect as well. When substituting x = -54 into the original equation, the left-hand side becomes ½(-54) + 9, which equals -27 + 9, or -18. The right-hand side, -2/3(-54), results in 36, thus the two sides do not equate.

Conclusion

The correct answer, x = -54/7, accurately satisfies the equation when both sides are evaluated. All other options fail to fulfill the equation's requirements, as demonstrated by substituting them back into the original equation, leading to mismatched results.