To solve 2

—

5

x = 14, you multiply both sides of the equation

by 5

—

2?

Yes, that's correct! To solve the equation 

\[
\frac{2}{5}x = 14,
\]

you can multiply both sides by the reciprocal of \(\frac{2}{5}\), which is \(\frac{5}{2}\). This will isolate \(x\) on one side of the equation. Let's go through the steps to solve it.

### Step-by-Step Solution

1. **Given Equation**:
   \[
   \frac{2}{5}x = 14
   \]

2. **Multiply both sides by the reciprocal of \(\frac{2}{5}\), which is \(\frac{5}{2}\)**:
   \[
   \left(\frac{5}{2}\right) \cdot \left(\frac{2}{5}x\right) = 14 \cdot \left(\frac{5}{2}\right)
   \]

3. **Simplify the left side**:
   \[
   x = 14 \cdot \frac{5}{2}
   \]

4. **Calculate the right side**:
   \[
   x = 14 \cdot \frac{5}{2} = \frac{14 \times 5}{2} = \frac{70}{2} = 35
   \]

### Answer

The value of \(x\) is **35**.

Would you like more details, or do you have any questions?

### Related Questions

1. How would you solve the equation \(\frac{3}{4}x = 12\)?
2. What is the process for solving \(4x = 20\) using multiplication or division?
3. How do you solve an equation where \(x\) is in the denominator, like \(\frac{x}{3} = 7\)?
4. What is the result if you multiply both sides of the equation \(2x = 10\) by \(\frac{1}{2}\)?
5. How do you solve equations that have multiple steps, such as \(2(x + 3) = 18\)?

**Tip:** When solving equations involving fractions, using the reciprocal to eliminate fractions is a helpful strategy to isolate the variable.

Learn how to solve the equation (2/5)x = 14 with a detailed step-by-step solution. This problem covers key algebraic concepts including equations involving fractions and multiplication. Suitable for students in Grades 7-9.

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