Understanding The Solution Of 1/X+1/3 1/5

Ex 6.1, 16 Solve (2x 1)/3 >= (3x 2)/4 (2 x)/5 from www.teachoo.com

Introduction

When it comes to mathematics, there are certain problems that require a deeper understanding of the concept. One such problem is the solution of 1/x+1/3 1/5. This problem can be confusing for students who are not familiar with the rules of fractions and algebra. In this article, we’ll discuss the problem in detail and provide a step-by-step solution.

Understanding the Problem

The problem 1/x+1/3 1/5 requires us to find the value of x. This problem involves adding three fractions and solving for an unknown variable. The first step to solving this problem is to understand the rules of fractions. When adding fractions, we need to have a common denominator. In this case, we need to find a common denominator for 1/x, 1/3, and 1/5.

Finding a Common Denominator

To find a common denominator, we need to look for the least common multiple (LCM) of the denominators. The denominators in this problem are x, 3, and 5. The LCM of 3 and 5 is 15. To get a common denominator of 15, we need to multiply each fraction by a factor that will result in a denominator of 15.

For 1/x, we need to multiply both the numerator and denominator by 15. This gives us 15/x. For 1/3, we need to multiply both the numerator and denominator by 5. This gives us 5/15. For 1/5, we need to multiply both the numerator and denominator by 3. This gives us 3/15.

Adding the Fractions

Now that we have a common denominator of 15, we can add the fractions. The equation now becomes 15/x + 5/15 + 3/15. We can simplify this equation by adding the numerators and keeping the denominator the same.

15/x + 5/15 + 3/15 = (15 + 5 + 3)/15 = 23/15

Cross-Multiplication

To solve for x, we need to use cross-multiplication. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of another fraction. In this case, we can use the first and second fractions to get:

15/x = 5/15

Solving for x

Now we can solve for x by cross-multiplying and simplifying the equation:

15(5) = 5(x)

75 = 5x

x = 15

Conclusion

In conclusion, the solution of 1/x+1/3 1/5 involves finding a common denominator, adding the fractions, and solving for x using cross-multiplication. This problem can be confusing for students who are not familiar with the rules of fractions and algebra. However, by following these steps, we can easily find the solution. It is important to understand the concept of fractions and the rules of algebra to solve these kinds of problems. Practice is key, and with enough practice, anyone can master these concepts.