(x/y)-z=rw
Solve for x in the equation above.
A.
X=y(z+rw)
B.
X=rw(y-z)
C.
X=rwy+z
D.
X=rwy-z
The correct answer and Explanation is :
To solve for ( x ) in the equation ( \frac{x}{y} – z = rw ), let’s break it down step by step.
Step 1: Start with the original equation
[
\frac{x}{y} – z = rw
]
We want to isolate ( x ) on one side of the equation. To do this, we first eliminate ( z ) by adding ( z ) to both sides of the equation:
[
\frac{x}{y} = rw + z
]
Step 2: Multiply both sides by ( y )
Next, multiply both sides of the equation by ( y ) to eliminate the denominator on the left-hand side:
[
x = y(rw + z)
]
This equation gives us the solution for ( x ).
Final Solution:
[
x = y(rw + z)
]
Answer:
The correct answer is A. ( x = y(z + rw) ).
Explanation:
The equation given is a combination of terms with fractions and variables. The goal is to isolate ( x ).
- Isolate ( x ):
By adding ( z ) to both sides, you move ( z ) away from the fraction ( \frac{x}{y} ), allowing you to focus on the term that contains ( x ). The equation becomes simpler and starts resembling a basic linear equation. - Eliminate the denominator:
By multiplying the entire equation by ( y ), you remove the fraction and now have a simpler equation in which ( x ) is isolated on one side. - Simplification:
After multiplying by ( y ), you’re left with ( x ) in terms of the other variables, which matches answer choice A.
This technique is widely used in algebra when working with fractions and helps ensure that the variable of interest is isolated in the final equation.