https://file.aiquickdraw.com/mathbot/file/1727049927631v9jqsxq6.jpg

The given equation is:

\[
\frac{x - 4}{5} - 9 = -6
\]

Let's solve it step-by-step.

### Step 1: Isolate the fraction term.
To do this, add 9 to both sides of the equation:

\[
\frac{x - 4}{5} - 9 + 9 = -6 + 9
\]

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

### Step 2: Eliminate the denominator.
Multiply both sides of the equation by 5 to get rid of the fraction:

\[
x - 4 = 3 \times 5
\]

\[
x - 4 = 15
\]

### Step 3: Solve for \( x \).
Add 4 to both sides:

\[
x - 4 + 4 = 15 + 4
\]

\[
x = 19
\]

Thus, the solution is \( x = 19 \).

Would you like any further details or clarifications?

Here are some follow-up questions to enhance your understanding:
1. How would the solution change if the constant on the right side were different?
2. Can you create a similar equation and solve it?
3. How do you verify the solution to this type of equation?
4. What happens if we have variables on both sides of the equation?
5. What if the fraction had a different denominator, like 10?

**Tip:** Always remember to check your solution by plugging it back into the original equation!

Solve the equation \(\frac{x-4}{5} - 9 = -6\).

Understand how to solve the linear equation \(\frac{x-4}{5} - 9 = -6\) through a step-by-step process. This problem covers key algebraic concepts such as isolating variables and eliminating fractions. Ideal for students in Grades 6-8.

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