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Simplifying 3(1 + -2x) + -5(3 + -1x) + -6(3x + -4) = 83 (1 * 3 + -2x * 3) + -5(3 + -1x) + -6(3x + -4) = 83 (3 + -6x) + -5(3 + -1x) + -6(3x + -4) = 83 3 + -6x + (3 * -5 + -1x * -5) + -6(3x + -4) = 83 3 + -6x + (-15 + 5x) + -6(3x + -4) = 83 Reorder the terms: 3 + -6x + -15 + 5x + -6(-4 + 3x) = 83 3 + -6x + -15 + 5x + (-4 * -6 + 3x * -6) = 83 3 + -6x + -15 + 5x + (24 + -18x) = 83 Reorder the terms: 3 + -15 + 24 + -6x + 5x + -18x = 83 Combine like terms: 3 + -15 = -12 -12 + 24 + -6x + 5x + -18x = 83 Combine like terms: -12 + 24 = 12 12 + -6x + 5x + -18x = 83 Combine like terms: -6x + 5x = -1x 12 + -1x + -18x = 83 Combine like terms: -1x + -18x = -19x 12 + -19x = 83 Solving 12 + -19x = 83 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -19x = 83 + -12 Combine like terms: 12 + -12 = 0 0 + -19x = 83 + -12 -19x = 83 + -12 Combine like terms: 83 + -12 = 71 -19x = 71 Divide each side by '-19'. x = -3.736842105 Simplifying x = -3.736842105
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