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Simplifying -5(1 + -5x) + 5(-8k + -2) = -4x + -8x (1 * -5 + -5x * -5) + 5(-8k + -2) = -4x + -8x (-5 + 25x) + 5(-8k + -2) = -4x + -8x Reorder the terms: -5 + 25x + 5(-2 + -8k) = -4x + -8x -5 + 25x + (-2 * 5 + -8k * 5) = -4x + -8x -5 + 25x + (-10 + -40k) = -4x + -8x Reorder the terms: -5 + -10 + -40k + 25x = -4x + -8x Combine like terms: -5 + -10 = -15 -15 + -40k + 25x = -4x + -8x Combine like terms: -4x + -8x = -12x -15 + -40k + 25x = -12x Solving -15 + -40k + 25x = -12x Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '15' to each side of the equation. -15 + -40k + 15 + 25x = 15 + -12x Reorder the terms: -15 + 15 + -40k + 25x = 15 + -12x Combine like terms: -15 + 15 = 0 0 + -40k + 25x = 15 + -12x -40k + 25x = 15 + -12x Add '-25x' to each side of the equation. -40k + 25x + -25x = 15 + -12x + -25x Combine like terms: 25x + -25x = 0 -40k + 0 = 15 + -12x + -25x -40k = 15 + -12x + -25x Combine like terms: -12x + -25x = -37x -40k = 15 + -37x Divide each side by '-40'. k = -0.375 + 0.925x Simplifying k = -0.375 + 0.925x
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