Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
Solution
-
Multiply both sides of the equation by
to eliminate the denominator: This simplifies to: -
Expand the right side:
-
Add
to both sides to isolate the term with : -
Divide both sides by
to solve for : -
Simplify the fraction:
The solution is
.
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The Deep Dive
To solve for
in the equation
, start by multiplying both sides by
to eliminate the fraction:
This expands to:
Next, add
to both sides:
Finally, divide both sides by
:
So, the solution is
.
In a real-world context, this type of equation could represent a scenario where you need to determine a variable, like the number of items produced or thresholds that involve fractions and scaling. It’s common in fields ranging from finance to engineering, where optimizing conditions and resources are key!
Remember to check your solution by substituting
back into the original equation. It’s a common mistake to forget this, but verifying can catch errors early—turning potential misunderstandings into learning opportunities!