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- Since \(|x | = 5\) means that the distance of \(x\) is 5 units from zero, then \(x=-5\) and \(x= 5\)
- Since \(|x-3| = 5\) means that the quantity of \((x-3) \) is 5 units from zero, then \((x-3)= 5\) or \((x-3) = -5\). Solving each equation, we find that \(x = 8\) or \(x = -2\)
- \(|2x-3| = 5\) means that \((2x-3 )= 5 \) or \((2x-3) = -5\). Solving each equation, we find that \(x = 4\) or \(x = -1\)
- \(|x | = -5\) means that the distance from zero is \(-5\), but distance is always positive therefore there is no solution.

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