To solve the equation \( \frac{3}{2}x + 5 = 14 \), we'll follow these steps:

1. **Isolate the term with \(x\)**: Start by subtracting 5 from both sides of the equation.
   
   \[
   \frac{3}{2}x + 5 - 5 = 14 - 5
   \]

   Simplifying this, we get:

   \[
   \frac{3}{2}x = 9
   \]

2. **Solve for \(x\)**: Multiply both sides by the reciprocal of \(\frac{3}{2}\) to isolate \(x\).

   \[
   x = 9 \times \frac{2}{3}
   \]

   Simplify the multiplication:

   \[
   x = \frac{18}{3}
   \]

   Simplifying further, we find:

   \[
   x = 6
   \]

### Solution

The value of \(x\) is **6**.

Would you like more details or have any questions?

Here are some related questions to explore further:

1. How would the solution change if the equation were \(\frac{3}{2}x - 5 = 14\)?
2. What happens if the coefficient of \(x\) was \(\frac{5}{2}\) instead of \(\frac{3}{2}\)?
3. How can you verify that \(x = 6\) is the correct solution for the given equation?
4. Can you graph the equation \(y = \frac{3}{2}x + 5\) and find where it intersects \(y = 14\)?
5. What are some common mistakes to avoid when solving equations like \(\frac{3}{2}x + 5 = 14\)?

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

Learn how to solve the equation 3/2x + 5 = 14 with detailed step-by-step instructions. This problem involves linear equations and fractional equations, suitable for students in 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