Solve `abs(x- 13)= 5` for x.

Options

A. 18
B. 8 or 18
C. `-18`
D. 8

Answer

To solve the equation \( |x - 13| = 5 \), we can follow these steps:

### Step 1: Understand the Absolute Value Equation
The equation \( |A| = B \) implies two cases:
1. \( A = B \)
2. \( A = -B \)

In our case, \( A = x - 13 \) and \( B = 5 \). Thus, we can write:
1. \( x - 13 = 5 \)
2. \( x - 13 = -5 \)

### Step 2: Solve the First Case
Starting with the first equation:
\[ x - 13 = 5 \]
Add 13 to both sides:
\[ x = 5 + 13 \]
\[ x = 18 \]

### Step 3: Solve the Second Case
Now, we solve the second equation:
\[ x - 13 = -5 \]
Add 13 to both sides:
\[ x = -5 + 13 \]
\[ x = 8 \]

### Step 4: Conclusion
The solutions to the equation \( |x - 13| = 5 \) are:
\[ x = 18 \quad \text{and} \quad x = 8 \]

### Final Answer
Thus, the values of \( x \) are \( 18 \) and \( 8 \).

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