Solve the following equations with absolute values in them.
`|x+2|=5`

Answer

To solve the equation \( |x + 2| = 5 \), we will follow these steps:

### Step 1: Understand the Absolute Value Equation
The absolute value equation \( |A| = B \) implies that \( A = B \) or \( A = -B \). In our case, \( A = x + 2 \) and \( B = 5 \).

### Step 2: Set Up Two Equations
From the absolute value equation, we can set up two separate equations:
1. \( x + 2 = 5 \)
2. \( x + 2 = -5 \)

### Step 3: Solve the First Equation
Now, we will solve the first equation:
\[ x + 2 = 5 \]
Subtract 2 from both sides:
\[ x = 5 - 2 \]
\[ x = 3 \]

### Step 4: Solve the Second Equation
Next, we will solve the second equation:
\[ x + 2 = -5 \]
Again, subtract 2 from both sides:
\[ x = -5 - 2 \]
\[ x = -7 \]

### Step 5: Write the Final Solution
The solutions to the equation \( |x + 2| = 5 \) are:
\[ x = 3 \quad \text{or} \quad x = -7 \]

### Final Answer:
Thus, the final solution is:
\[ x = 3 \quad \text{or} \quad x = -7 \]

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