What are two different ways  2/3x =10 could be solved for x? 

To solve the equation \( \frac{2}{3}x = 10 \) for \( x \), here are two different methods:

### Method 1: Multiply by the reciprocal of \( \frac{2}{3} \)
1. Start with the equation:
   \[
   \frac{2}{3}x = 10
   \]
2. Multiply both sides of the equation by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \):
   \[
   x = 10 \times \frac{3}{2}
   \]
3. Simplify the right-hand side:
   \[
   x = \frac{30}{2} = 15
   \]

### Method 2: Eliminate the fraction by multiplying both sides by 3
1. Start with the equation:
   \[
   \frac{2}{3}x = 10
   \]
2. Multiply both sides by 3 to eliminate the denominator:
   \[
   2x = 30
   \]
3. Now, divide both sides by 2:
   \[
   x = \frac{30}{2} = 15
   \]

Both methods give the solution \( x = 15 \).

Do you want further details on any of these methods or have any questions?

### Related questions:
1. How do you solve equations involving fractions and variables?
2. What does multiplying by the reciprocal mean in algebra?
3. How can fractions be cleared from both sides of an equation?
4. What is the general approach to solving linear equations?
5. What happens when a fraction has a variable in both the numerator and denominator?

**Tip:** When solving equations involving fractions, multiplying by the reciprocal is often the quickest way to isolate the variable.

What are two different ways 2/3x = 10 could be solved for x?

Explore two methods to solve the linear equation 2/3x = 10 for x. This guide covers multiplying by the reciprocal and eliminating fractions, using key algebraic concepts like properties of equality. Ideal for students in Grades 6-8.

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