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Simplifying -11(k + 12) + -3(9k + 1) = -11k + -12k Reorder the terms: -11(12 + k) + -3(9k + 1) = -11k + -12k (12 * -11 + k * -11) + -3(9k + 1) = -11k + -12k (-132 + -11k) + -3(9k + 1) = -11k + -12k Reorder the terms: -132 + -11k + -3(1 + 9k) = -11k + -12k -132 + -11k + (1 * -3 + 9k * -3) = -11k + -12k -132 + -11k + (-3 + -27k) = -11k + -12k Reorder the terms: -132 + -3 + -11k + -27k = -11k + -12k Combine like terms: -132 + -3 = -135 -135 + -11k + -27k = -11k + -12k Combine like terms: -11k + -27k = -38k -135 + -38k = -11k + -12k Combine like terms: -11k + -12k = -23k -135 + -38k = -23k Solving -135 + -38k = -23k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '23k' to each side of the equation. -135 + -38k + 23k = -23k + 23k Combine like terms: -38k + 23k = -15k -135 + -15k = -23k + 23k Combine like terms: -23k + 23k = 0 -135 + -15k = 0 Add '135' to each side of the equation. -135 + 135 + -15k = 0 + 135 Combine like terms: -135 + 135 = 0 0 + -15k = 0 + 135 -15k = 0 + 135 Combine like terms: 0 + 135 = 135 -15k = 135 Divide each side by '-15'. k = -9 Simplifying k = -9
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