https://file.aiquickdraw.com/mathbot/file/1726873163923sakchjyn.jpg

The equation shown in the image is:

\[ 32 = |-7 + 2x| \times 8 \]

Let's solve this step-by-step.

1. First, isolate the absolute value expression:
\[
|-7 + 2x| = \frac{32}{8}
\]
\[
|-7 + 2x| = 4
\]

2. The absolute value equation \( |-7 + 2x| = 4 \) splits into two cases:

**Case 1:** 
\[
-7 + 2x = 4
\]
Solve for \( x \):
\[
2x = 4 + 7
\]
\[
2x = 11
\]
\[
x = \frac{11}{2} = 5.5
\]

**Case 2:** 
\[
-7 + 2x = -4
\]
Solve for \( x \):
\[
2x = -4 + 7
\]
\[
2x = 3
\]
\[
x = \frac{3}{2} = 1.5
\]

So, the solutions for \( x \) are:

\[
x = 5.5 \quad \text{and} \quad x = 1.5
\]

Would you like more details or have any other questions?

Here are 5 related questions you might find useful:
1. How do you graph absolute value equations?
2. What is the significance of absolute values in equations?
3. How do absolute value inequalities differ from absolute value equations?
4. Can you provide an example of a real-world problem involving absolute values?
5. How do transformations affect the graph of an absolute value function?

**Tip:** When solving absolute value equations, always remember to split into two cases to account for both positive and negative scenarios inside the absolute value.

Learn how to solve the absolute value equation 32 = |-7 + 2x| × 8 with step-by-step guidance. This problem covers key algebraic concepts and absolute value equations. Suitable for students in Grades 9-11.

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