https://file.aiquickdraw.com/mathbot/file/17285649835254f50ts9y.jpg

Let's solve the equation shown in the image:

\[
-10 = \frac{-3(x - 9) + 4}{-4}
\]

### Step 1: Simplify the denominator
The denominator is \(-4\), so we can multiply both sides of the equation by \(-4\) to eliminate the fraction:

\[
-10 \times (-4) = -3(x - 9) + 4
\]

This simplifies to:

\[
40 = -3(x - 9) + 4
\]

### Step 2: Isolate the term with \(x\)
Next, subtract 4 from both sides:

\[
40 - 4 = -3(x - 9)
\]

\[
36 = -3(x - 9)
\]

### Step 3: Solve for \(x\)
Now divide both sides by \(-3\) to isolate \(x - 9\):

\[
\frac{36}{-3} = x - 9
\]

\[
-12 = x - 9
\]

Finally, add 9 to both sides to solve for \(x\):

\[
x = -12 + 9
\]

\[
x = -3
\]

So the solution is:

\[
x = -3
\]

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. How would the solution change if the fraction in the original equation had a different denominator?
2. What happens if we change the constant on the right side of the equation?
3. How would the steps change if there were additional terms involving \(x\) outside the fraction?
4. How would you solve this equation if the numerator was a quadratic expression?
5. Can you create a similar equation but with a positive denominator and solve it?

**Tip:** When solving equations with fractions, multiplying both sides by the denominator is an efficient way to clear the fraction early in the solution.

Learn how to solve the linear equation -10 = (-3(x - 9) + 4) / -4 step by step. This problem includes concepts of algebra, fractions, and simplification techniques, suitable for Grades 8-10.

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