To solve the equation \(-2|h-7| = -28\), we can first isolate the absolute value term.
- Divide both sides by \(-2\): \[ |h-7| = \frac{-28}{-2} = 14 \]
Now we have the equation: \[ |h-7| = 14 \]
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Next, we solve the absolute value equation, which gives us two cases:
Case 1: \[ h - 7 = 14 \] Solving for \(h\): \[ h = 14 + 7 = 21 \]
Case 2: \[ h - 7 = -14 \] Solving for \(h\): \[ h = -14 + 7 = -7 \]
Thus, the solutions to the equation \(-2|h-7| = -28\) are: \[ h = 21 \quad \text{or} \quad h = -7 \]
So the final answer is: \[ h = 21 \quad \text{and} \quad h = -7 \]