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Simplifying -3(2x + -4) + 5(4x + -7) + -1 = 6(x + 8) + 0.5(-4x + -4) Reorder the terms: -3(-4 + 2x) + 5(4x + -7) + -1 = 6(x + 8) + 0.5(-4x + -4) (-4 * -3 + 2x * -3) + 5(4x + -7) + -1 = 6(x + 8) + 0.5(-4x + -4) (12 + -6x) + 5(4x + -7) + -1 = 6(x + 8) + 0.5(-4x + -4) Reorder the terms: 12 + -6x + 5(-7 + 4x) + -1 = 6(x + 8) + 0.5(-4x + -4) 12 + -6x + (-7 * 5 + 4x * 5) + -1 = 6(x + 8) + 0.5(-4x + -4) 12 + -6x + (-35 + 20x) + -1 = 6(x + 8) + 0.5(-4x + -4) Reorder the terms: 12 + -35 + -1 + -6x + 20x = 6(x + 8) + 0.5(-4x + -4) Combine like terms: 12 + -35 = -23 -23 + -1 + -6x + 20x = 6(x + 8) + 0.5(-4x + -4) Combine like terms: -23 + -1 = -24 -24 + -6x + 20x = 6(x + 8) + 0.5(-4x + -4) Combine like terms: -6x + 20x = 14x -24 + 14x = 6(x + 8) + 0.5(-4x + -4) Reorder the terms: -24 + 14x = 6(8 + x) + 0.5(-4x + -4) -24 + 14x = (8 * 6 + x * 6) + 0.5(-4x + -4) -24 + 14x = (48 + 6x) + 0.5(-4x + -4) Reorder the terms: -24 + 14x = 48 + 6x + 0.5(-4 + -4x) -24 + 14x = 48 + 6x + (-4 * 0.5 + -4x * 0.5) -24 + 14x = 48 + 6x + (-2 + -2x) Reorder the terms: -24 + 14x = 48 + -2 + 6x + -2x Combine like terms: 48 + -2 = 46 -24 + 14x = 46 + 6x + -2x Combine like terms: 6x + -2x = 4x -24 + 14x = 46 + 4x Solving -24 + 14x = 46 + 4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4x' to each side of the equation. -24 + 14x + -4x = 46 + 4x + -4x Combine like terms: 14x + -4x = 10x -24 + 10x = 46 + 4x + -4x Combine like terms: 4x + -4x = 0 -24 + 10x = 46 + 0 -24 + 10x = 46 Add '24' to each side of the equation. -24 + 24 + 10x = 46 + 24 Combine like terms: -24 + 24 = 0 0 + 10x = 46 + 24 10x = 46 + 24 Combine like terms: 46 + 24 = 70 10x = 70 Divide each side by '10'. x = 7 Simplifying x = 7
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