Question

5.
$z = \frac{x + 3}{2y}$
the given equation relates the distinct positive real numbers $x$, $y$, and $z$. which equation correctly expresses $x$ in terms of $y$ and $z$?
a) $x = 2yz + 3$
b) $x = 2yz - 3$
c) $x = \frac{z}{2y} - 3$
d) $x = \frac{z - 3}{2y}$

Explanation:

Step1: Multiply both sides by \(2y\)

To eliminate the denominator on the right - hand side, we multiply both sides of the equation \(z=\frac{x + 3}{2y}\) by \(2y\). Using the property of equality \(a=b\Rightarrow a\times c=b\times c\) (where \(c = 2y\) and \(y
eq0\) since \(y\) is a positive real number), we get:
\(z\times2y=\frac{x + 3}{2y}\times2y\)
Simplifying the right - hand side, the \(2y\) in the numerator and denominator cancels out, and we have \(2yz=x + 3\)

Step2: Subtract 3 from both sides

To solve for \(x\), we use the property of equality \(a=b\Rightarrow a - c=b - c\) (where \(c = 3\)). Subtract 3 from both sides of the equation \(2yz=x + 3\):
\(2yz-3=x + 3-3\)
Simplifying the right - hand side, we get \(x=2yz - 3\)

Answer:

B) \(x = 2yz-3\)