If  −x/3+5x/6=−1/2
 , what is the value of 6x
?

To solve the equation \(-\frac{x}{3} + \frac{5x}{6} = -\frac{1}{2}\), we'll follow these steps:

1. **Find a common denominator** for the fractions involving \(x\). The common denominator for \(3\) and \(6\) is \(6\).

   - Rewrite \(-\frac{x}{3}\) as \(-\frac{2x}{6}\).

   Now, the equation becomes:
   \[
   -\frac{2x}{6} + \frac{5x}{6} = -\frac{1}{2}
   \]

2. **Combine like terms** on the left side:
   \[
   \frac{5x}{6} - \frac{2x}{6} = \frac{3x}{6}
   \]
   Simplifying this gives:
   \[
   \frac{x}{2} = -\frac{1}{2}
   \]

3. **Solve for \(x\)** by multiplying both sides by 2:
   \[
   x = -1
   \]

4. **Find the value of \(6x\)**:
   \[
   6x = 6(-1) = -6
   \]

So, the value of \(6x\) is \(-6\).

Would you like more details or have any other questions?

Here are 5 related questions:
1. How would the solution change if the equation were \(-\frac{x}{3} + \frac{5x}{6} = \frac{1}{2}\)?
2. What is the general method for solving linear equations with fractions?
3. How do you handle equations where variables appear in both numerators and denominators?
4. Can you explain how to find the common denominator in more complex equations?
5. How would you solve the equation if it were in the form \(-\frac{x}{3} + \frac{5}{6} = -\frac{1}{2}\)?

**Tip:** Always simplify fractions and combine like terms before solving the equation. This can make the process much easier and reduce errors.

Learn how to solve the equation -x/3 + 5x/6 = -1/2 with detailed steps and explanations. This problem involves fractions and algebraic manipulation. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation