Solve the equation for x: ½ x + 9 = -2/3 x

Rationale

x = -54/7

To solve the equation \( \frac{1}{2}x + 9 = -\frac{2}{3}x \), we first eliminate the fractions by multiplying through by a common denominator. This leads us to isolate \( x \) and find that \( x = -\frac{54}{7} \).

A (x=-9/7) YOUR ANSWER

This choice does not satisfy the original equation. Plugging \( x = -\frac{9}{7} \) into the left-hand side gives \( \frac{1}{2}(-\frac{9}{7}) + 9 \), which does not equal \( -\frac{2}{3}(-\frac{9}{7}) \). Therefore, this value is incorrect.

B (x=-54/7) CORRECT

Substituting \( x = -\frac{54}{7} \) back into the original equation verifies the solution. The left-hand side simplifies to \( \frac{1}{2}(-\frac{54}{7}) + 9 \), which exactly equals \( -\frac{2}{3}(-\frac{54}{7}) \), confirming that this is indeed the correct answer.

C (x=-6) YOUR ANSWER

When substituting \( x = -6 \) into the original equation, the left-hand side becomes \( \frac{1}{2}(-6) + 9 = 6 \), while the right-hand side calculates to \( -\frac{2}{3}(-6) = 4 \). Since both sides do not match, this value is incorrect.

D (x=-54) YOUR ANSWER

For \( x = -54 \), substituting into the original equation yields \( \frac{1}{2}(-54) + 9 = -27 + 9 = -18 \) for the left-hand side, and \( -\frac{2}{3}(-54) = 36 \) for the right-hand side. Since these results are not equal, this option is also incorrect.

Conclusion

The solution to the equation \( \frac{1}{2}x + 9 = -\frac{2}{3}x \) is \( x = -\frac{54}{7} \). All other options do not satisfy the equation when substituted, confirming that choice B is the only valid solution. This process illustrates the importance of verifying solutions through substitution to ensure correctness.

Solve the equation for x: ½ x + 9 = -2/3 x

x = -54/7

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test