2x-3.        -x-1
——— =   ———
2                            4

Let's solve the equation:

\[
\frac{2x - 3}{2} = \frac{-x - 1}{4}
\]

### Step 1: Eliminate the denominators
To eliminate the fractions, multiply both sides of the equation by the least common denominator (LCD) of 2 and 4, which is 4.

\[
4 \times \frac{2x - 3}{2} = 4 \times \frac{-x - 1}{4}
\]

Simplifying both sides:

\[
2(2x - 3) = -x - 1
\]

### Step 2: Distribute
Now, distribute the 2 on the left-hand side:

\[
4x - 6 = -x - 1
\]

### Step 3: Move all terms involving \(x\) to one side
Add \(x\) to both sides to move the \(x\)-terms together:

\[
4x + x - 6 = -1
\]

Simplifying:

\[
5x - 6 = -1
\]

### Step 4: Solve for \(x\)
Add 6 to both sides to isolate the \(x\)-term:

\[
5x = 5
\]

Now, divide by 5:

\[
x = 1
\]

### Final Answer:
The solution to the equation is \(x = 1\).

Would you like a detailed explanation of any step or have further questions?

Here are 5 related questions you can explore:
1. How can I verify if \(x = 1\) is the correct solution?
2. What happens if both sides of an equation have different denominators?
3. How would the solution change if the equation was \(\frac{2x - 3}{2} = \frac{-x - 2}{4}\)?
4. What is the importance of distributing in equations like this?
5. How can I solve equations with variables on both sides?

**Tip:** Always check your solution by substituting the value of \(x\) back into the original equation.

Learn how to solve the linear equation 2x - 3 / 2 = -x - 1 / 4 by eliminating fractions, using the distributive property, and isolating variables. This detailed step-by-step solution is suitable for students in Grades 8-10.

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