−1−( 
3 
2 
​
 x−1)−9x=
3 
4 
​

We are given the equation:

\[
-1 - \left(\frac{3}{2}x - 1\right) - 9x = \frac{3}{4}
\]

Let's solve it step by step:

### Step 1: Simplify the expression on the left side
We distribute the negative sign across \(\left(\frac{3}{2}x - 1\right)\):

\[
-1 - \frac{3}{2}x + 1 - 9x = \frac{3}{4}
\]

Now, simplify the constants:

\[
-1 + 1 = 0
\]

This reduces the equation to:

\[
-\frac{3}{2}x - 9x = \frac{3}{4}
\]

### Step 2: Combine like terms
The terms on the left side are both \(x\) terms. We can combine them by finding a common denominator:

\[
-\frac{3}{2}x - 9x = -\frac{3}{2}x - \frac{18}{2}x = -\frac{21}{2}x
\]

Now, the equation is:

\[
-\frac{21}{2}x = \frac{3}{4}
\]

### Step 3: Solve for \(x\)
To isolate \(x\), multiply both sides by \(-\frac{2}{21}\):

\[
x = \frac{3}{4} \times -\frac{2}{21}
\]

Simplifying:

\[
x = \frac{3 \times -2}{4 \times 21} = \frac{-6}{84} = \frac{-1}{14}
\]

### Final Answer:
\[
x = \frac{-1}{14}
\]

Would you like more details on any step or further clarification?

---

Here are 5 related questions:
1. How do you handle equations with multiple variables?
2. What is the importance of finding a common denominator in combining fractions?
3. How does distributing a negative sign affect terms within parentheses?
4. What steps are involved in simplifying complex equations?
5. How can you check your solution for accuracy?

**Tip**: Always double-check your work by plugging your solution back into the original equation to verify it is correct.

Explore the step-by-step process of solving the linear equation -1 - (3/2x - 1) - 9x = 3/4. This solution involves algebraic concepts such as combining like terms, working with fractions, and applying the distributive property. Suitable for students in Grades 8-10.

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