https://file.aiquickdraw.com/mathbot/file/1725491827161bfnak3bg.jpg

The problem in the image asks you to find the solution for the equation:

\[
\frac{1}{5}x + 6 = -12
\]

Let's solve this step by step.

### Step 1: Isolate the term with the variable \( x \)
We start by subtracting 6 from both sides of the equation to move the constant term on the left side over to the right side.

\[
\frac{1}{5}x + 6 - 6 = -12 - 6
\]

Simplifying this, we get:

\[
\frac{1}{5}x = -18
\]

### Step 2: Eliminate the fraction
To eliminate the fraction, multiply both sides of the equation by 5:

\[
5 \times \frac{1}{5}x = -18 \times 5
\]

Simplifying this:

\[
x = -90
\]

### Solution
The solution to the equation is \( x = -90 \).

Would you like to know more details about this process, or do you have any questions?

Here are 5 related questions to deepen your understanding:
1. What would be the solution if the fraction had a different denominator, like \(\frac{1}{3}\)?
2. How do you solve the equation if it were \(\frac{2}{5}x + 6 = -12\)?
3. What happens if you have a negative fraction, such as \(-\frac{1}{5}x + 6 = -12\)?
4. Can you explain how to solve \(\frac{1}{5}x - 6 = -12\)?
5. What would be the first step if there were more terms on both sides of the equation?

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

Learn how to solve the linear equation (1/5)x + 6 = -12 step by step. This problem covers essential algebraic concepts like isolating variables and eliminating fractions. Suitable for students in Grades 6-8.

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