Select the correct answer.
Which value of [tex]$n$[/tex] makes this equation true?
[tex]\frac{3 n+3}{5}=\frac{3 n-1}{5}[/tex]
A. [tex]$n=-16$[/tex]
B. [tex]$n=-2$[/tex]
C. [tex]$n=2$[/tex]
D. [tex]$n=16$[/tex]
Answer (1)
Multiply both sides of the equation by 5: 3 n + 3 = 3 n − 1 .
Subtract 3 n from both sides: 3 = − 1 .
The equation 3 = − 1 is a contradiction.
There is no solution: $\boxed{\text{No solution}}.
Explanation
Problem Analysis We are given the equation 5 3 n + 3 = 5 3 n − 1 and asked to find the value of n that makes the equation true. Let's solve the equation step by step.
Eliminating Fractions First, we can multiply both sides of the equation by 5 to eliminate the fractions: 5 × 5 3 n + 3 = 5 × 5 3 n − 1
This simplifies to: 3 n + 3 = 3 n − 1
Isolating n Next, we want to isolate n . We can subtract 3 n from both sides of the equation: 3 n + 3 − 3 n = 3 n − 1 − 3 n
This simplifies to: 3 = − 1
Analyzing the Result The equation 3 = − 1 is a contradiction, which means there is no value of n that can make the original equation true. Therefore, there is no solution to the equation.
Conclusion Since there is no value of n that satisfies the equation, none of the given options are correct.
Examples
This problem demonstrates how to solve linear equations with fractions. In real life, you might use similar techniques to solve problems involving proportions, such as scaling recipes or converting units. For example, if you need to adjust the amount of ingredients in a recipe to serve a different number of people, you would set up a proportion and solve for the unknown quantities. Understanding how to manipulate equations and solve for variables is a fundamental skill in many areas of science, engineering, and everyday life.
