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Simplifying 5(13 + -31x) + -3(40x + 100) = 1 + -9x + 2(17 + 2x) (13 * 5 + -31x * 5) + -3(40x + 100) = 1 + -9x + 2(17 + 2x) (65 + -155x) + -3(40x + 100) = 1 + -9x + 2(17 + 2x) Reorder the terms: 65 + -155x + -3(100 + 40x) = 1 + -9x + 2(17 + 2x) 65 + -155x + (100 * -3 + 40x * -3) = 1 + -9x + 2(17 + 2x) 65 + -155x + (-300 + -120x) = 1 + -9x + 2(17 + 2x) Reorder the terms: 65 + -300 + -155x + -120x = 1 + -9x + 2(17 + 2x) Combine like terms: 65 + -300 = -235 -235 + -155x + -120x = 1 + -9x + 2(17 + 2x) Combine like terms: -155x + -120x = -275x -235 + -275x = 1 + -9x + 2(17 + 2x) -235 + -275x = 1 + -9x + (17 * 2 + 2x * 2) -235 + -275x = 1 + -9x + (34 + 4x) Reorder the terms: -235 + -275x = 1 + 34 + -9x + 4x Combine like terms: 1 + 34 = 35 -235 + -275x = 35 + -9x + 4x Combine like terms: -9x + 4x = -5x -235 + -275x = 35 + -5x Solving -235 + -275x = 35 + -5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5x' to each side of the equation. -235 + -275x + 5x = 35 + -5x + 5x Combine like terms: -275x + 5x = -270x -235 + -270x = 35 + -5x + 5x Combine like terms: -5x + 5x = 0 -235 + -270x = 35 + 0 -235 + -270x = 35 Add '235' to each side of the equation. -235 + 235 + -270x = 35 + 235 Combine like terms: -235 + 235 = 0 0 + -270x = 35 + 235 -270x = 35 + 235 Combine like terms: 35 + 235 = 270 -270x = 270 Divide each side by '-270'. x = -1 Simplifying x = -1
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