Let's solve the equation step by step:

Given equation:

\[
\frac{3}{2}X + 4 \times \left(-1 + \frac{8X}{5}\right) = 1
\]

### Step 1: Distribute the 4 across the terms inside the parentheses
\[
\frac{3}{2}X + 4(-1) + 4\left(\frac{8X}{5}\right) = 1
\]

This simplifies to:

\[
\frac{3}{2}X - 4 + \frac{32X}{5} = 1
\]

### Step 2: Combine like terms
To combine \(\frac{3}{2}X\) and \(\frac{32X}{5}\), find a common denominator, which is 10.

Convert each term:
\[
\frac{3}{2}X = \frac{15X}{10}
\]
\[
\frac{32X}{5} = \frac{64X}{10}
\]

Now combine them:
\[
\frac{15X}{10} + \frac{64X}{10} = \frac{79X}{10}
\]

So the equation becomes:
\[
\frac{79X}{10} - 4 = 1
\]

### Step 3: Isolate the variable term
Add 4 to both sides:
\[
\frac{79X}{10} = 5
\]

### Step 4: Solve for \(X\)
Multiply both sides by \(\frac{10}{79}\):
\[
X = \frac{50}{79}
\]

Thus, the solution is:

\[
X = \frac{50}{79}
\]

Would you like any additional details or have any questions?

### Related Questions:
1. What happens if the equation includes a different variable?
2. How would you solve this equation if the coefficient of \(X\) was negative?
3. Can you solve this equation using a different method?
4. How do you handle an equation with more complex fractions?
5. What is the significance of isolating the variable?

### Tip:
When dealing with fractions in equations, finding a common denominator early on can simplify the process of combining like terms.

Learn how to solve the equation 3/2X + 4 x (-1+8X/5)=1 with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations, distributive property, combining like terms, isolating variables, and handling fractions. Suitable for high school students.

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