Solve for $x$:
$\frac{4}{x}+\frac{2}{-1}=\frac{6}{x}$
Enter your answer as a reduced fraction.
Answer (1)
Simplify the equation: x 4 − 2 = x 6 .
Subtract x 4 from both sides: − 2 = x 6 − x 4 .
Combine terms: − 2 = x 2 .
Solve for x : x = − 2 2 = − 1 .
The solution is − 1 .
Explanation
Understanding the Problem We are given the equation x 4 + − 1 2 = x 6 . Our goal is to solve for x and express the answer as a reduced fraction.
Simplifying the Equation First, simplify the equation by rewriting − 1 2 as − 2 . The equation becomes x 4 − 2 = x 6 .
Isolating the Constant Next, subtract x 4 from both sides of the equation to isolate the constant term. This gives us − 2 = x 6 − x 4 .
Combining Terms Combine the terms on the right side of the equation: − 2 = x 6 − 4 , which simplifies to − 2 = x 2 .
Removing the Fraction Multiply both sides of the equation by x to get rid of the fraction: − 2 x = 2 .
Solving for x Finally, divide both sides of the equation by − 2 to solve for x : x = − 2 2 .
Simplifying the Solution Simplify the fraction to get x = − 1 .
Examples
Imagine you're distributing flyers for a local event. If you know that one person can distribute flyers at a certain rate, this problem helps you determine how many people you need to distribute a certain number of flyers in a given time. By setting up an equation similar to the one above, you can solve for the number of people needed to achieve your goal. This kind of problem-solving is useful in many real-world scenarios, such as planning events, managing resources, or coordinating tasks.
