Question

the correct method to begin solving \\(\frac{x}{y} = z + a\\) for \\(x\\) is:
a. divide both sides by \\(z\\)
b. subtract \\(a\\) from both sides
c. add \\(a\\) to both sides
d. multiply both sides by \\(y\\)

Explanation:

To solve \(\frac{x}{y}=z + a\) for \(x\), we need to isolate \(x\). The term with \(x\) is \(\frac{x}{y}\), so to get \(x\) alone, we can multiply both sides by \(y\) (since multiplying both sides of an equation by the same non - zero number \(y\) preserves the equality). Let's analyze the other options:

• Option a: Dividing both sides by \(z\) will not help in isolating \(x\) as \(x\) is not multiplied by \(z\) in the original equation.
• Option b: Subtracting \(a\) from both sides will give \(\frac{x}{y}-a=z\), which does not isolate \(x\).
• Option c: Adding \(a\) to both sides will give \(\frac{x}{y}+a = z + 2a\), which also does not isolate \(x\).
• Option d: If we multiply both sides of \(\frac{x}{y}=z + a\) by \(y\), we get \(x=y(z + a)\), which is the first step to solve for \(x\).

Answer:

d. Multiply both sides by \(y\)