https://file.aiquickdraw.com/mathbot/file/1725400229910vm8dfgor.jpg

The equation provided is:

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

Let's solve this step by step.

### Step 1: Simplify the equation
Subtract 3 from both sides:

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

### Step 2: Solve for the absolute value expression
Divide both sides by -2:

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

### Step 3: Solve the absolute value equation
The absolute value of a number is zero only if the number inside the absolute value is zero. So:

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

### Step 4: Solve for \( s \)
Add 5 to both sides:

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

Multiply both sides by 4 to solve for \( s \):

\[
s = 20
\]

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

Would you like further details or have any questions about this solution? 

Here are five related questions to consider:

1. How would the solution change if the constant outside the absolute value were positive instead of negative?
2. What would happen if the equation included an additional term outside the absolute value?
3. How can you solve an equation where the expression inside the absolute value is a quadratic instead of linear?
4. What if the absolute value term included a variable on both sides of the equation?
5. How would you graph the function that represents the original equation?

**Tip:** When solving equations with absolute values, always consider the possibility of multiple cases, particularly when the expression inside the absolute value might be negative.

Learn how to solve the absolute value equation 3 = -2|1/4s - 5| + 3 step-by-step. This problem covers key algebraic concepts, including absolute value properties and linear equations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation