Solve the equation. 2x+5/8 + x-3/8 = x+4/6. What is the solution set?

To solve the equation:

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

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

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

So, the equation simplifies to:

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

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

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

This simplifies to:

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

Distribute both sides:

\[ 9x + 6 = 4(x + 4) \]

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

Next, isolate the variable \(x\). Subtract \(4x\) from both sides:

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

\[ 5x + 6 = 16 \]

Subtract 6 from both sides:

\[ 5x = 10 \]

Finally, divide by 5:

\[ x = 2 \]

Thus, the solution set is:

\[ \{2\} \]

Would you like any details or have any questions?

Here are 8 related questions:

1. What steps are involved in combining fractions with the same denominator?
2. How can you find the least common multiple (LCM) of two numbers?
3. Why is it useful to clear fractions when solving an equation?
4. How do you distribute multiplication over addition and subtraction within parentheses?
5. What are the steps to isolate a variable in a linear equation?
6. How do you verify a solution to an equation?
7. What techniques can be used to solve equations with multiple fractions?
8. How do you handle equations with variables on both sides?

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

Learn how to solve the equation 2x + 5/8 + x - 3/8 = x + 4/6 with detailed step-by-step instructions. This problem involves combining fractions, using the distributive property, and isolating variables. Suitable for high school students.

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