$\frac{3}{c-2}=\frac{3}{2 c-5}$
Answer (1)
Set the denominators equal to each other: c − 2 = 2 c − 5 .
Subtract c from both sides: − 2 = c − 5 .
Add 5 to both sides: 3 = c .
The solution is 3 .
Explanation
Understanding the Problem We are given the equation c − 2 3 = 2 c − 5 3 . Our goal is to find the value of c that satisfies this equation. Since the numerators on both sides of the equation are equal (both are 3), the denominators must also be equal for the equation to hold true.
Setting Denominators Equal To find the value of c , we set the denominators equal to each other: c − 2 = 2 c − 5
Isolating c Now, we solve the equation c − 2 = 2 c − 5 for c . First, subtract c from both sides of the equation: c − 2 − c = 2 c − 5 − c − 2 = c − 5
Solving for c Next, add 5 to both sides of the equation: − 2 + 5 = c − 5 + 5 3 = c So, c = 3 .
Verification To check our solution, we substitute c = 3 back into the original equation: 3 − 2 3 = 2 ( 3 ) − 5 3 1 3 = 6 − 5 3 3 = 1 3 3 = 3 Since the equation holds true, our solution is correct.
Final Answer Therefore, the value of c that satisfies the equation c − 2 3 = 2 c − 5 3 is 3 .
Examples
Imagine you're balancing a seesaw. The equation c − 2 3 = 2 c − 5 3 is like finding the exact point ( c ) where two weights are perfectly balanced. In real life, this could apply to balancing chemical equations, designing stable structures, or even optimizing resource allocation to ensure equilibrium. Understanding how to solve such equations helps in various fields where balance and equality are crucial.
