Let's solve the equation step by step:

Given equation:
\[
a + \frac{4}{3} - \frac{a}{7} = a + \frac{7}{5}
\]

1. **Subtract \(a\) from both sides** to simplify:
   \[
   \frac{4}{3} - \frac{a}{7} = \frac{7}{5}
   \]

2. **Isolate the term involving \(a\)** by moving \(\frac{4}{3}\) to the other side:
   \[
   -\frac{a}{7} = \frac{7}{5} - \frac{4}{3}
   \]

3. **Find a common denominator** to subtract the fractions on the right side:
   - The common denominator for \(5\) and \(3\) is \(15\).
   \[
   \frac{7}{5} = \frac{21}{15}, \quad \frac{4}{3} = \frac{20}{15}
   \]
   So,
   \[
   \frac{7}{5} - \frac{4}{3} = \frac{21}{15} - \frac{20}{15} = \frac{1}{15}
   \]

   Therefore:
   \[
   -\frac{a}{7} = \frac{1}{15}
   \]

4. **Multiply both sides by \(-7\)** to solve for \(a\):
   \[
   a = -\frac{7}{15}
   \]

So, the solution is:
\[
a = -\frac{7}{15}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the solution change if the equation were \(a + \frac{4}{3} - \frac{a}{7} = 2a + \frac{7}{5}\)?
2. Can you solve the equation \(\frac{3}{4}x + \frac{2}{3} = x - \frac{5}{6}\)?
3. What happens if you replace \(a\) with a different variable, like \(b\), in the equation?
4. How can you verify the solution \(a = -\frac{7}{15}\) by substituting it back into the original equation?
5. What is the importance of finding a common denominator when dealing with fractions in equations?

**Tip:** When dealing with fractions in equations, finding a common denominator simplifies subtraction or addition and helps in isolating variables.

Learn how to solve the equation a + 4/3 - a/7 = a + 7/5 step-by-step with detailed explanations. This problem covers solving equations with fractions and involves isolating variables. Suitable for students in Grades 7-9.

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