https://file.aiquickdraw.com/mathbot/file/1726751595345vck6k1ts.jpg

The equation given in the image is:

\[
53 = |c - 1| - 1
\]

Let's solve for \( c \):

### Step 1: Isolate the absolute value expression
Add 1 to both sides to eliminate the \(-1\) on the right-hand side:

\[
53 + 1 = |c - 1|
\]

\[
54 = |c - 1|
\]

### Step 2: Solve for \( c \) using the definition of absolute value

The absolute value equation \( |c - 1| = 54 \) gives two possible cases:

- **Case 1:** \( c - 1 = 54 \)
- **Case 2:** \( c - 1 = -54 \)

### Step 3: Solve both cases

- **For Case 1:**
  \[
  c - 1 = 54
  \]
  Add 1 to both sides:
  \[
  c = 55
  \]

- **For Case 2:**
  \[
  c - 1 = -54
  \]
  Add 1 to both sides:
  \[
  c = -53
  \]

### Final Answer:
The two possible values for \( c \) are:

\[
c = 55 \quad \text{or} \quad c = -53
\]

Would you like further details or explanations on any part of this solution?

### Related Questions:
1. How do you solve absolute value equations in general?
2. What happens if the equation inside the absolute value has no real solution?
3. Can absolute value equations have more than two solutions?
4. What is the difference between absolute value and modulus in mathematics?
5. How would the solution change if the equation had a coefficient multiplying the absolute value?

### Tip:
Always check your solutions by substituting them back into the original equation to ensure they satisfy the conditions.

Learn how to solve the absolute value equation 53 = |c - 1| - 1 with a clear step-by-step solution. Understand the properties of absolute values and how to handle multiple cases in this algebraic problem, suitable for Grades 8-10.

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