https://file.aiquickdraw.com/mathbot/file/1726802641006r3rqqkuj.jpg

The image contains three algebraic equations. Let's go through each one and solve them step by step.

1. **First equation**:
   \[
   \frac{3x}{10} - x = \frac{1}{2} - \frac{x}{5}
   \]
   
2. **Second equation**:
   \[
   \frac{5x}{6} - 4 = \frac{2x}{3} - \frac{3x}{2}
   \]

3. **Third equation**:
   \[
   \frac{3x}{10} - \frac{5}{2} = \frac{x}{6} - \frac{1}{2}
   \]

I will start solving these equations one by one.The solutions to the three equations are:

1. For the first equation \(\frac{3x}{10} - x = \frac{1}{2} - \frac{x}{5}\), the solution is \(x = -1\).

2. For the second equation \(\frac{5x}{6} - 4 = \frac{2x}{3} - \frac{3x}{2}\), the solution is \(x = 2.4\).

3. For the third equation \(\frac{3x}{10} - \frac{5}{2} = \frac{x}{6} - \frac{1}{2}\), the solution is \(x = 15\).

Would you like more details or further explanations on any of the solutions?

Here are some related questions for further practice:

1. What happens if we substitute \(x = -1\) in the first equation?
2. How do we approach solving equations with fractions step by step?
3. What is the importance of finding a common denominator when dealing with fractional equations?
4. How can you verify if your solution is correct in these types of equations?
5. What would be the result if the terms on both sides were multiplied by a common factor to eliminate fractions?

**Tip:** When solving equations with fractions, it is helpful to clear the fractions early by multiplying through by the least common denominator.

The image contains three algebraic equations:
1. \(\frac{3x}{10} - x = \frac{1}{2} - \frac{x}{5}\)
2. \(\frac{5x}{6} - 4 = \frac{2x}{3} - \frac{3x}{2}\)
3. \(\frac{3x}{10} - \frac{5}{2} = \frac{x}{6} - \frac{1}{2}\)

Learn how to solve algebraic equations involving fractions and variables with detailed step-by-step solutions. This problem covers key algebraic concepts, including cross-multiplication, balancing equations, and the properties of equality. Suitable for students in Grades 8-10.

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