Determine z in the equation 1/(6z) = 2/9

Rationale

z equals 12/9 in the equation 1/(6z) = 2/9.

To solve for z, we first cross-multiply the equation, which leads to 1 = (2/9) * (6z). Simplifying this gives us z = 12/9 after isolating z.

A (18-Feb) YOUR ANSWER

This choice simplifies to 9, which does not satisfy the equation when substituted back in. The value of z must be derived from the equation, and 18/2 does not yield the correct relationship.

B (Feb-54) YOUR ANSWER

This choice simplifies to 1/27, which when substituted back into the equation does not hold true. The calculated value of z must be 12/9, making this option incorrect.

C (12-Sept) CORRECT

This is the correct answer as it simplifies to 4/3. When substituting z = 12/9 back into the original equation, both sides equate, confirming its validity as the solution to the equation.

D (09-Dec) YOUR ANSWER

This choice simplifies to 3/4, which does not satisfy the original equation upon substitution. The correct value of z derived from the equation is 12/9, making this option incorrect.

Conclusion

The solution to the equation 1/(6z) = 2/9 reveals that z equals 12/9, or 4/3. This value is derived through cross-multiplication and simplification, confirming its correctness when checked against the original equation. The other answer choices do not satisfy the equation, emphasizing the importance of correctly manipulating algebraic expressions to find valid solutions.

Determine z in the equation 1/(6z) = 2/9

z equals 12/9 in the equation 1/(6z) = 2/9.

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