Let's solve the equation step by step:

The given equation is:

\[
3 = -2\left|\frac{1}{4}s - 5\right| + 3
\]

### Step 1: Subtract 3 from both sides
First, eliminate the constant on the right-hand side by subtracting 3 from both sides:

\[
3 - 3 = -2\left|\frac{1}{4}s - 5\right| + 3 - 3
\]

This simplifies to:

\[
0 = -2\left|\frac{1}{4}s - 5\right|
\]

### Step 2: Divide by -2
Next, divide both sides of the equation by -2 to isolate the absolute value term:

\[
\frac{0}{-2} = \left|\frac{1}{4}s - 5\right|
\]

This simplifies to:

\[
0 = \left|\frac{1}{4}s - 5\right|
\]

### Step 3: Solve the absolute value
The absolute value of any expression is 0 if and only if the expression inside the absolute value is 0. So:

\[
\frac{1}{4}s - 5 = 0
\]

### Step 4: Solve for \( s \)
Add 5 to both sides to get rid of the constant:

\[
\frac{1}{4}s = 5
\]

Now, multiply both sides by 4 to solve for \( s \):

\[
s = 5 \times 4 = 20
\]

### Final Answer:
The solution to the equation is \( s = 20 \).

Would you like further explanation or additional details?

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Here are 5 related questions to explore further:

1. What are the properties of absolute value equations?
2. How do you handle absolute value inequalities?
3. Can absolute value equations have multiple solutions?
4. How would this equation change if the coefficient of the absolute value term was positive?
5. How do we solve equations involving fractions and variables inside absolute values?

**Tip:** Always check your solution when solving absolute value equations by plugging it back into the original equation.

Learn how to solve the absolute value equation 3 = -2|1/4s - 5| + 3 with a clear step-by-step explanation. This example demonstrates the process of solving equations involving absolute values and linear terms. Suitable for students in Grades 8-10.

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