To solve the equation
\[ \frac{3}{2}(4 - 8x) + 5x = 1 - 7x, \]
we will apply the properties of equality step by step.
Step 1: Distribute \(\frac{3}{2}\)
Using the distributive property:
\[ \frac{3}{2} \cdot 4 - \frac{3}{2} \cdot 8x + 5x = 1 - 7x. \]
This simplifies to:
\[ 6 - 12x + 5x = 1 - 7x. \]
Step 2: Combine like terms on the left side
Now we combine the \(x\) terms:
\[ 6 - 12x + 5x = 6 - 7x. \]
So, we rewrite the equation as:
\[ 6 - 7x = 1 - 7x. \]
Step 3: Add \(7x\) to both sides
Next, we can add \(7x\) to both sides to simplify further:
\[ 6 - 7x + 7x = 1 - 7x + 7x. \]
This simplifies to:
\[ 6 = 1. \]
Step 4: Analyze the result
At this point, we see that the equation \(6 = 1\) is not true. This indicates that there are no values of \(x\) that can satisfy the original equation.
Conclusion:
The original equation has no solutions. In summary, we applied the properties of equality to manipulate the equation step by step and found that it leads to a contradiction. Thus, the number of solutions to the equation is:
\[ \boxed{0}. \]