Solve the equation. 2x+5/8 + x-3/8 = x+4/6

To solve the equation:

\[ \frac{2x + 5}{8} + \frac{x - 3}{8} = \frac{x + 4}{6} \]

First, combine the terms on the left-hand side:

\[ \frac{2x + 5}{8} + \frac{x - 3}{8} = \frac{(2x + 5) + (x - 3)}{8} = \frac{3x + 2}{8} \]

Now, the equation is:

\[ \frac{3x + 2}{8} = \frac{x + 4}{6} \]

To clear the fractions, find the least common multiple (LCM) of 8 and 6, which is 24. Multiply both sides of the equation by 24:

\[ 24 \cdot \frac{3x + 2}{8} = 24 \cdot \frac{x + 4}{6} \]

This simplifies to:

\[ 3 \cdot (3x + 2) = 4 \cdot (x + 4) \]

Now distribute:

\[ 9x + 6 = 4x + 16 \]

Subtract \(4x\) from both sides:

\[ 9x - 4x + 6 = 16 \]

Simplify:

\[ 5x + 6 = 16 \]

Subtract 6 from both sides:

\[ 5x = 10 \]

Divide both sides by 5:

\[ x = 2 \]

So, the solution to the equation is:

\[ x = 2 \]

Would you like any details or have any questions?

Here are 8 related questions:

1. What are the steps to combine fractions with the same denominator?
2. How do you find the least common multiple (LCM) of two numbers?
3. Why is it important to clear fractions in an equation?
4. How do you distribute multiplication over addition within parentheses?
5. What is the process to isolate a variable in an equation?
6. How do you verify if a solution to an equation is correct?
7. What are the methods to solve equations with multiple variables?
8. How can you solve equations that involve fractions with different denominators?

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

Learn how to solve the equation 2x + 5/8 + x - 3/8 = x + 4/6 with a detailed step-by-step solution. This problem covers equations with fractions, combining like terms, and finding the least common multiple (LCM). Suitable for students in Grades 7-9.

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