We are given the equation:

\[
- |8 - 5x| - 10 = -19
\]

### Step 1: Simplify the equation
First, add 10 to both sides to isolate the absolute value expression:

\[
- |8 - 5x| = -19 + 10
\]

\[
- |8 - 5x| = -9
\]

### Step 2: Remove the negative sign
To eliminate the negative sign, multiply both sides of the equation by -1:

\[
|8 - 5x| = 9
\]

### Step 3: Solve the absolute value equation
We now solve for two cases because the absolute value can result in either a positive or a negative value:

1. **Case 1**: \(8 - 5x = 9\)
   
   Subtract 8 from both sides:
   
   \[
   -5x = 1
   \]
   
   Divide by -5:
   
   \[
   x = -\frac{1}{5}
   \]

2. **Case 2**: \(8 - 5x = -9\)
   
   Subtract 8 from both sides:
   
   \[
   -5x = -17
   \]
   
   Divide by -5:
   
   \[
   x = \frac{17}{5}
   \]

### Step 4: Final solutions
Thus, the solutions are:

\[
x = -\frac{1}{5} \quad \text{or} \quad x = \frac{17}{5}
\]

Would you like further explanation or details on any of the steps?

Here are 5 related questions:
1. How do you solve absolute value inequalities?
2. Can absolute values ever be negative?
3. How does multiplying both sides of an equation affect the solution?
4. How do you verify solutions in absolute value equations?
5. What are some applications of absolute value in real life?

**Tip:** Always check for extraneous solutions when solving absolute value equations by substituting your solutions back into the original equation.

Learn how to solve the absolute value equation −|8−5x|−10=−19 with a detailed step-by-step solution. This problem explores algebraic concepts, including absolute value properties and solving for variables. Suitable for students in Grades 8-10.

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