what is the complete solution to the equation |8-4x|=40?

To solve the equation \( |8 - 4x| = 40 \), we need to consider the definition of absolute value. The absolute value equation \( |A| = B \) implies that either \( A = B \) or \( A = -B \).

So, we break the equation into two cases:

### Case 1: \( 8 - 4x = 40 \)
\[
8 - 4x = 40
\]
Subtract 8 from both sides:
\[
-4x = 32
\]
Divide by -4:
\[
x = -8
\]

### Case 2: \( 8 - 4x = -40 \)
\[
8 - 4x = -40
\]
Subtract 8 from both sides:
\[
-4x = -48
\]
Divide by -4:
\[
x = 12
\]

### Solutions:
The complete solution to the equation \( |8 - 4x| = 40 \) is:
\[
x = -8 \quad \text{or} \quad x = 12
\]

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you solve absolute value equations with variables on both sides?
2. What happens if the equation inside the absolute value has no solution?
3. How would the solution change if the equation was \( |8 - 4x| = -40 \)?
4. How can you graph the equation \( |8 - 4x| = 40 \)?
5. What is the significance of absolute value in real-world scenarios?

**Tip:** When solving absolute value equations, always remember to consider both the positive and negative scenarios to ensure all possible solutions are found.

Discover the complete solution to the equation |8-4x|=40 with a detailed step-by-step explanation. Learn how to solve absolute value equations involving linear equations and algebraic methods. Suitable for Grades 7-9 students and anyone interested in algebraic problem-solving.

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