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Simplifying 4(5k + -5) + 19 = -9 + 2(3k + -8) Reorder the terms: 4(-5 + 5k) + 19 = -9 + 2(3k + -8) (-5 * 4 + 5k * 4) + 19 = -9 + 2(3k + -8) (-20 + 20k) + 19 = -9 + 2(3k + -8) Reorder the terms: -20 + 19 + 20k = -9 + 2(3k + -8) Combine like terms: -20 + 19 = -1 -1 + 20k = -9 + 2(3k + -8) Reorder the terms: -1 + 20k = -9 + 2(-8 + 3k) -1 + 20k = -9 + (-8 * 2 + 3k * 2) -1 + 20k = -9 + (-16 + 6k) Combine like terms: -9 + -16 = -25 -1 + 20k = -25 + 6k Solving -1 + 20k = -25 + 6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6k' to each side of the equation. -1 + 20k + -6k = -25 + 6k + -6k Combine like terms: 20k + -6k = 14k -1 + 14k = -25 + 6k + -6k Combine like terms: 6k + -6k = 0 -1 + 14k = -25 + 0 -1 + 14k = -25 Add '1' to each side of the equation. -1 + 1 + 14k = -25 + 1 Combine like terms: -1 + 1 = 0 0 + 14k = -25 + 1 14k = -25 + 1 Combine like terms: -25 + 1 = -24 14k = -24 Divide each side by '14'. k = -1.714285714 Simplifying k = -1.714285714
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