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Simplifying 3x + 9x + -6x + 1000 = 3x + 5(-1x + 100) Reorder the terms: 1000 + 3x + 9x + -6x = 3x + 5(-1x + 100) Combine like terms: 3x + 9x = 12x 1000 + 12x + -6x = 3x + 5(-1x + 100) Combine like terms: 12x + -6x = 6x 1000 + 6x = 3x + 5(-1x + 100) Reorder the terms: 1000 + 6x = 3x + 5(100 + -1x) 1000 + 6x = 3x + (100 * 5 + -1x * 5) 1000 + 6x = 3x + (500 + -5x) Reorder the terms: 1000 + 6x = 500 + 3x + -5x Combine like terms: 3x + -5x = -2x 1000 + 6x = 500 + -2x Solving 1000 + 6x = 500 + -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. 1000 + 6x + 2x = 500 + -2x + 2x Combine like terms: 6x + 2x = 8x 1000 + 8x = 500 + -2x + 2x Combine like terms: -2x + 2x = 0 1000 + 8x = 500 + 0 1000 + 8x = 500 Add '-1000' to each side of the equation. 1000 + -1000 + 8x = 500 + -1000 Combine like terms: 1000 + -1000 = 0 0 + 8x = 500 + -1000 8x = 500 + -1000 Combine like terms: 500 + -1000 = -500 8x = -500 Divide each side by '8'. x = -62.5 Simplifying x = -62.5
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