Find the value of k.
`45 - [28 - {37 - (15 - k)}] = 58`

Answer

To find the value of \( k \) in the equation

\[ 45 - [28 - \{37 - (15 - k)\}] = 58, \]

we will solve it step by step.

### Step 1: Simplify the innermost parentheses
Start with the innermost expression \( 15 - k \).

### Step 2: Substitute back into the equation
Now substitute \( 15 - k \) back into the equation:

\[ 45 - [28 - \{37 - (15 - k)\}] = 58 \]

This becomes:

\[ 45 - [28 - (37 - (15 - k))] = 58 \]

### Step 3: Simplify the expression inside the curly braces
Now simplify \( 37 - (15 - k) \):

\[ 37 - 15 + k = 22 + k \]

### Step 4: Substitute back into the equation
Now substitute \( 22 + k \) back into the equation:

\[ 45 - [28 - (22 + k)] = 58 \]

### Step 5: Simplify the expression inside the square brackets
Now simplify \( 28 - (22 + k) \):

\[ 28 - 22 - k = 6 - k \]

### Step 6: Substitute back into the equation
Now substitute \( 6 - k \) back into the equation:

\[ 45 - (6 - k) = 58 \]

### Step 7: Simplify the equation
Now simplify \( 45 - (6 - k) \):

\[ 45 - 6 + k = 39 + k \]

### Step 8: Set the equation equal to 58
Now we have:

\[ 39 + k = 58 \]

### Step 9: Solve for \( k \)
Subtract 39 from both sides:

\[ k = 58 - 39 \]

\[ k = 19 \]

Thus, the value of \( k \) is \( 19 \).

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