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Simplifying 4(2k + -5) + -5(4k + 1) = 2 + -2(k + 3) Reorder the terms: 4(-5 + 2k) + -5(4k + 1) = 2 + -2(k + 3) (-5 * 4 + 2k * 4) + -5(4k + 1) = 2 + -2(k + 3) (-20 + 8k) + -5(4k + 1) = 2 + -2(k + 3) Reorder the terms: -20 + 8k + -5(1 + 4k) = 2 + -2(k + 3) -20 + 8k + (1 * -5 + 4k * -5) = 2 + -2(k + 3) -20 + 8k + (-5 + -20k) = 2 + -2(k + 3) Reorder the terms: -20 + -5 + 8k + -20k = 2 + -2(k + 3) Combine like terms: -20 + -5 = -25 -25 + 8k + -20k = 2 + -2(k + 3) Combine like terms: 8k + -20k = -12k -25 + -12k = 2 + -2(k + 3) Reorder the terms: -25 + -12k = 2 + -2(3 + k) -25 + -12k = 2 + (3 * -2 + k * -2) -25 + -12k = 2 + (-6 + -2k) Combine like terms: 2 + -6 = -4 -25 + -12k = -4 + -2k Solving -25 + -12k = -4 + -2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2k' to each side of the equation. -25 + -12k + 2k = -4 + -2k + 2k Combine like terms: -12k + 2k = -10k -25 + -10k = -4 + -2k + 2k Combine like terms: -2k + 2k = 0 -25 + -10k = -4 + 0 -25 + -10k = -4 Add '25' to each side of the equation. -25 + 25 + -10k = -4 + 25 Combine like terms: -25 + 25 = 0 0 + -10k = -4 + 25 -10k = -4 + 25 Combine like terms: -4 + 25 = 21 -10k = 21 Divide each side by '-10'. k = -2.1 Simplifying k = -2.1
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