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Simplifying 5(x + 1) + -2(5 + x) + 4 = 2(100 + x) + -206 Reorder the terms: 5(1 + x) + -2(5 + x) + 4 = 2(100 + x) + -206 (1 * 5 + x * 5) + -2(5 + x) + 4 = 2(100 + x) + -206 (5 + 5x) + -2(5 + x) + 4 = 2(100 + x) + -206 5 + 5x + (5 * -2 + x * -2) + 4 = 2(100 + x) + -206 5 + 5x + (-10 + -2x) + 4 = 2(100 + x) + -206 Reorder the terms: 5 + -10 + 4 + 5x + -2x = 2(100 + x) + -206 Combine like terms: 5 + -10 = -5 -5 + 4 + 5x + -2x = 2(100 + x) + -206 Combine like terms: -5 + 4 = -1 -1 + 5x + -2x = 2(100 + x) + -206 Combine like terms: 5x + -2x = 3x -1 + 3x = 2(100 + x) + -206 -1 + 3x = (100 * 2 + x * 2) + -206 -1 + 3x = (200 + 2x) + -206 Reorder the terms: -1 + 3x = 200 + -206 + 2x Combine like terms: 200 + -206 = -6 -1 + 3x = -6 + 2x Solving -1 + 3x = -6 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -1 + 3x + -2x = -6 + 2x + -2x Combine like terms: 3x + -2x = 1x -1 + 1x = -6 + 2x + -2x Combine like terms: 2x + -2x = 0 -1 + 1x = -6 + 0 -1 + 1x = -6 Add '1' to each side of the equation. -1 + 1 + 1x = -6 + 1 Combine like terms: -1 + 1 = 0 0 + 1x = -6 + 1 1x = -6 + 1 Combine like terms: -6 + 1 = -5 1x = -5 Divide each side by '1'. x = -5 Simplifying x = -5
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