$\frac{1}{7}+\frac{1}{x}=\frac{1}{4}$
Answer (1)
Subtract 7 1 from both sides: x 1 = 4 1 − 7 1 .
Find a common denominator: x 1 = 28 7 − 28 4 .
Simplify: x 1 = 28 3 .
Take the reciprocal: x = 3 28 .
The solution is 3 28 .
Explanation
Problem Analysis We are given the equation 7 1 + x 1 = 4 1 . Our goal is to find the value of x that satisfies this equation.
Isolating the Term with x First, we want to isolate the term with x . To do this, we subtract 7 1 from both sides of the equation: x 1 = 4 1 − 7 1
Finding a Common Denominator Next, we need to find a common denominator for the right side of the equation. The least common multiple of 4 and 7 is 28, so we rewrite the fractions with the common denominator: x 1 = 28 7 − 28 4
Simplifying the Equation Now, we simplify the right side of the equation by subtracting the fractions: x 1 = 28 7 − 4 = 28 3
Solving for x To solve for x , we take the reciprocal of both sides of the equation: x = 3 28
Final Answer Therefore, the value of x that satisfies the equation is 3 28 .
Examples
Imagine you are dividing a task between two people. One person can complete 7 1 of the task per hour, and together, you want to complete 4 1 of the task per hour. This problem helps you determine how much of the task the second person needs to complete per hour. Understanding how to solve such equations is crucial in resource allocation and time management, ensuring efficient collaboration and task completion.
