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The equation you provided is:

\[
\frac{2 - 3x}{4} = 5
\]

Let's solve it step by step:

### Step 1: Eliminate the denominator
Multiply both sides of the equation by 4 to get rid of the denominator:
\[
2 - 3x = 5 \times 4
\]
\[
2 - 3x = 20
\]

### Step 2: Isolate the variable term
Subtract 2 from both sides:
\[
-3x = 20 - 2
\]
\[
-3x = 18
\]

### Step 3: Solve for \( x \)
Divide both sides by -3:
\[
x = \frac{18}{-3}
\]
\[
x = -6
\]

Thus, the solution is:
\[
x = -6
\]

Would you like any additional details on these steps or explanations? Here are five related questions that could extend this problem:

1. How would the solution change if the denominator were a different number, say 5?
2. Can you solve for \( x \) if the equation is \( \frac{2 - 3x}{4} = -5 \)?
3. What happens if you add a constant to both sides of the equation before solving?
4. Can you create a similar equation but with a quadratic expression in the numerator?
5. How would you approach solving the equation if the fraction included a variable in the denominator as well?

### Tip:
When solving linear equations, always try to first eliminate fractions by multiplying both sides by the denominator to simplify the equation.

Solve the linear equation (2 - 3x) / 4 = 5 with a detailed step-by-step guide. Learn how to eliminate denominators, isolate variables, and find the value of x. Suitable for students in Grades 7-8.

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