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Simplifying 5(2x + -1) + 3(x + -1) + -6(7x + -12) = 15(8 + -1x) + -84 Reorder the terms: 5(-1 + 2x) + 3(x + -1) + -6(7x + -12) = 15(8 + -1x) + -84 (-1 * 5 + 2x * 5) + 3(x + -1) + -6(7x + -12) = 15(8 + -1x) + -84 (-5 + 10x) + 3(x + -1) + -6(7x + -12) = 15(8 + -1x) + -84 Reorder the terms: -5 + 10x + 3(-1 + x) + -6(7x + -12) = 15(8 + -1x) + -84 -5 + 10x + (-1 * 3 + x * 3) + -6(7x + -12) = 15(8 + -1x) + -84 -5 + 10x + (-3 + 3x) + -6(7x + -12) = 15(8 + -1x) + -84 Reorder the terms: -5 + 10x + -3 + 3x + -6(-12 + 7x) = 15(8 + -1x) + -84 -5 + 10x + -3 + 3x + (-12 * -6 + 7x * -6) = 15(8 + -1x) + -84 -5 + 10x + -3 + 3x + (72 + -42x) = 15(8 + -1x) + -84 Reorder the terms: -5 + -3 + 72 + 10x + 3x + -42x = 15(8 + -1x) + -84 Combine like terms: -5 + -3 = -8 -8 + 72 + 10x + 3x + -42x = 15(8 + -1x) + -84 Combine like terms: -8 + 72 = 64 64 + 10x + 3x + -42x = 15(8 + -1x) + -84 Combine like terms: 10x + 3x = 13x 64 + 13x + -42x = 15(8 + -1x) + -84 Combine like terms: 13x + -42x = -29x 64 + -29x = 15(8 + -1x) + -84 64 + -29x = (8 * 15 + -1x * 15) + -84 64 + -29x = (120 + -15x) + -84 Reorder the terms: 64 + -29x = 120 + -84 + -15x Combine like terms: 120 + -84 = 36 64 + -29x = 36 + -15x Solving 64 + -29x = 36 + -15x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15x' to each side of the equation. 64 + -29x + 15x = 36 + -15x + 15x Combine like terms: -29x + 15x = -14x 64 + -14x = 36 + -15x + 15x Combine like terms: -15x + 15x = 0 64 + -14x = 36 + 0 64 + -14x = 36 Add '-64' to each side of the equation. 64 + -64 + -14x = 36 + -64 Combine like terms: 64 + -64 = 0 0 + -14x = 36 + -64 -14x = 36 + -64 Combine like terms: 36 + -64 = -28 -14x = -28 Divide each side by '-14'. x = 2 Simplifying x = 2
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