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Simplifying 4 + -5(1 + 4k) = -37 + -8k 4 + (1 * -5 + 4k * -5) = -37 + -8k 4 + (-5 + -20k) = -37 + -8k Combine like terms: 4 + -5 = -1 -1 + -20k = -37 + -8k Solving -1 + -20k = -37 + -8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '8k' to each side of the equation. -1 + -20k + 8k = -37 + -8k + 8k Combine like terms: -20k + 8k = -12k -1 + -12k = -37 + -8k + 8k Combine like terms: -8k + 8k = 0 -1 + -12k = -37 + 0 -1 + -12k = -37 Add '1' to each side of the equation. -1 + 1 + -12k = -37 + 1 Combine like terms: -1 + 1 = 0 0 + -12k = -37 + 1 -12k = -37 + 1 Combine like terms: -37 + 1 = -36 -12k = -36 Divide each side by '-12'. k = 3 Simplifying k = 3
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