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Absolute value is a mathematician's way of judging numbers by their magnitude rather than their positive/negative value. It is the distance of the number from 0 on a number line.

What is the sum of all values of \(x\) that satisfy \[\lvert{x-2}\rvert=10?\]

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Find the sum of all the integer values of \(x\) that satisfy \[|x-49|+|x-50|=7?\]

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What is the value of \(x\) that satisfies \[2x^2+5 \lvert{x}\rvert+3=0 ?\]

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What is the value of \(x\) that satisfies the equation \[\lvert{x-11}\rvert=\lvert{25-x}\rvert?\]

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