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Simplifying 100(x + -100) + 99(x + -99) = 2 * 99 * 100 Reorder the terms: 100(-100 + x) + 99(x + -99) = 2 * 99 * 100 (-100 * 100 + x * 100) + 99(x + -99) = 2 * 99 * 100 (-10000 + 100x) + 99(x + -99) = 2 * 99 * 100 Reorder the terms: -10000 + 100x + 99(-99 + x) = 2 * 99 * 100 -10000 + 100x + (-99 * 99 + x * 99) = 2 * 99 * 100 -10000 + 100x + (-9801 + 99x) = 2 * 99 * 100 Reorder the terms: -10000 + -9801 + 100x + 99x = 2 * 99 * 100 Combine like terms: -10000 + -9801 = -19801 -19801 + 100x + 99x = 2 * 99 * 100 Combine like terms: 100x + 99x = 199x -19801 + 199x = 2 * 99 * 100 Multiply 2 * 99 -19801 + 199x = 198 * 100 Multiply 198 * 100 -19801 + 199x = 19800 Solving -19801 + 199x = 19800 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19801' to each side of the equation. -19801 + 19801 + 199x = 19800 + 19801 Combine like terms: -19801 + 19801 = 0 0 + 199x = 19800 + 19801 199x = 19800 + 19801 Combine like terms: 19800 + 19801 = 39601 199x = 39601 Divide each side by '199'. x = 199 Simplifying x = 199
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