To solve the equation \( \frac{1}{X} + \frac{1}{X} + 5 = \frac{1}{6} \), we can proceed with the following steps:

1. Combine the like terms on the left side:
   \[
   \frac{1}{X} + \frac{1}{X} = \frac{2}{X}
   \]
   So the equation simplifies to:
   \[
   \frac{2}{X} + 5 = \frac{1}{6}
   \]

2. Subtract 5 from both sides of the equation to isolate the fraction:
   \[
   \frac{2}{X} = \frac{1}{6} - 5
   \]

3. Express 5 as a fraction with a denominator of 6:
   \[
   \frac{1}{6} - \frac{30}{6} = \frac{1 - 30}{6} = \frac{-29}{6}
   \]
   So now, the equation is:
   \[
   \frac{2}{X} = \frac{-29}{6}
   \]

4. To solve for \( X \), multiply both sides by \( X \) and then divide by \(-29\):
   \[
   2 = \frac{-29X}{6}
   \]
   Multiply both sides by 6:
   \[
   12 = -29X
   \]
   Now, divide both sides by \(-29\):
   \[
   X = \frac{12}{-29} = -\frac{12}{29}
   \]

So, the solution is \( X = -\frac{12}{29} \).

Would you like more details or have any questions?

Here are some related questions to explore:

1. How would the solution change if the equation was \( \frac{1}{X} + \frac{1}{X} + 5 = \frac{1}{3} \)?
2. What is the process to solve a quadratic equation?
3. How do you solve an equation with multiple variables?
4. What are the applications of reciprocal functions in real-world problems?
5. How do you graph the equation \( y = \frac{2}{X} + 5 \)?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies all terms.

Learn how to solve the rational equation 1/X + 1/X + 5 = 1/6 step by step. This solution covers essential algebraic concepts such as combining like terms, solving rational equations, and dealing with fractions. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation