We are given the equation:

\[
\frac{1}{x} + \frac{1}{x} + 5 = \frac{1}{6}
\]

Let's solve for \( x \) step by step.

### Step 1: Combine the like terms
The two terms involving \( \frac{1}{x} \) can be combined:

\[
\frac{1}{x} + \frac{1}{x} = \frac{2}{x}
\]

Now the equation becomes:

\[
\frac{2}{x} + 5 = \frac{1}{6}
\]

### Step 2: Move the constant to the other side
Subtract 5 from both sides:

\[
\frac{2}{x} = \frac{1}{6} - 5
\]

To simplify the right-hand side, express 5 as a fraction with a denominator of 6:

\[
5 = \frac{30}{6}
\]

Now, subtract:

\[
\frac{2}{x} = \frac{1}{6} - \frac{30}{6} = \frac{-29}{6}
\]

### Step 3: Solve for \( x \)
Now, solve for \( x \) by multiplying both sides of the equation by \( x \) and then solving for \( x \):

\[
2 = \frac{-29x}{6}
\]

Multiply both sides by 6:

\[
12 = -29x
\]

Now, solve for \( x \):

\[
x = \frac{12}{-29}
\]

Thus, the value of \( x \) is:

\[
x = -\frac{12}{29}
\]

Would you like any more details or clarifications?

### Related Questions:
1. How can we verify that \( x = -\frac{12}{29} \) is correct?
2. What happens if we modify the original equation slightly, like changing the constant term?
3. What if instead of \( 1/6 \), the right-hand side was a different fraction?
4. How can we solve similar equations involving multiple fractions?
5. What are some methods for simplifying complex fractions?

### Tip:
When dealing with equations involving fractions, it often helps to find a common denominator or eliminate fractions early on by multiplying both sides by the least common denominator (LCD).

Learn how to solve the rational equation 1/x + 1/x + 5 = 1/6 step by step. This problem involves algebraic concepts like combining fractions and solving linear equations 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