Question
\( (a-b)\left(x^{\prime}-6\right)=a c-a a^{\prime} b+b c \)
Ask by Moreno Zimmerman. in India
Jan 08,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x' = \frac{a c - a a' b + b c}{a - b} + 6 \)
Solution
Sure, let's solve the equation for \( x' \):
\[
(a - b)(x' - 6) = a c - a a' b + b c
\]
### Step 1: Expand the Left Side
First, distribute \( (a - b) \) on the left side:
\[
(a - b)x' - 6(a - b) = a c - a a' b + b c
\]
### Step 2: Isolate the Term with \( x' \)
Add \( 6(a - b) \) to both sides to isolate the term containing \( x' \):
\[
(a - b)x' = a c - a a' b + b c + 6(a - b)
\]
### Step 3: Solve for \( x' \)
Divide both sides of the equation by \( (a - b) \) to solve for \( x' \):
\[
x' = \frac{a c - a a' b + b c + 6(a - b)}{a - b}
\]
### Step 4: Simplify the Expression
You can simplify the numerator by factoring or combining like terms if possible. However, without specific values for the variables, this is the most simplified form:
\[
x' = \frac{a c - a a' b + b c}{a - b} + 6
\]
### Final Solution
\[
x' = \frac{a c - a a' b + b c}{a - b} + 6
\]
This expression gives \( x' \) in terms of the other variables \( a \), \( b \), \( c \), and \( a' \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
This equation serves as a fascinating example of how algebra can model relationships in various contexts, such as physics or economics. For instance, \( a \) and \( b \) could represent quantities in a supply-demand model, while \( c \) could be a cost or revenue term reflecting changes in one variable impacting another. In practical terms, it’s vital to remember to clearly define your variables. For instance, if this equation pops up in a problem about rates, make sure to know what each symbol represents. A common mistake is assuming relationships without checking units or context – always keep an eye out for these little details!
