Question 14

x = y(nw + z)

To solve for x in the equation (x/y) - z = nw, we first isolate the term involving x, leading to the expression x = y(nw + z).

A) x = y(nw + z)

This option is correct because, starting from the equation (x/y) - z = nw, we can multiply both sides by y and then rearrange to find that x must equal y multiplied by the sum of nw and z.

B) x = y(2 + rw)

This option is incorrect as it introduces the arbitrary term "2" and "rw," which do not appear in the original equation and do not relate to the necessary manipulation of the terms to solve for x.

C) x = yw + yz

This option is incorrect because it suggests that x can be expressed as the sum of two products, yw and yz, which does not correctly follow from the original equation's structure and the necessary algebraic manipulations.

D) x = y(nw - z)

This option is incorrect as it misrepresents the relationship between the terms in the original equation. The correct manipulation of (x/y) - z does not yield a subtraction of z from nw but rather an addition.

Conclusion

Option A is definitively correct as it accurately represents the solution derived from the initial equation by applying proper algebraic methods. The other options fail to align with the mathematical operations required to isolate x, thereby confirming their inaccuracies.