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The given equation is:

\[
\frac{15x + 21}{3} = 5x + 7
\]

Let's simplify and solve it step-by-step:

1. **Simplify the left-hand side**:  
   \[
   \frac{15x + 21}{3} = 5x + 7 \implies 5x + 7 = 5x + 7
   \]

2. **Observe the simplified equation**:  
   After simplification, both sides of the equation are identical, which means the equation holds true for all values of \( x \).

3. **Determine the number of solutions**:  
   Since the equation is true for any value of \( x \), it has **infinitely many solutions**.

Therefore, the answer is:

**D. Infinitely many solutions**

Would you like further details or have any questions on this solution? Here are 5 related questions:

1. What is a consistent equation, and how does it differ from an inconsistent one?
2. How do you identify if an equation has infinitely many solutions?
3. What are some examples of linear equations with no solutions?
4. How do you solve equations involving fractions?
5. How can you verify the number of solutions for an equation graphically?

**Tip**: When both sides of an equation simplify to the same expression, it usually indicates infinitely many solutions.

How many solutions does this equation have: (15x + 21)/3 = 5x + 7?

Explore how to solve the linear equation (15x + 21)/3 = 5x + 7 with a detailed step-by-step solution. This problem demonstrates the concept of equations that are true for all values of x, leading to infinitely many solutions. Suitable for Grade 8 students.

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