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Simplifying -2k + -7(3k + 7) = -3(1 + 4k) + -2 Reorder the terms: -2k + -7(7 + 3k) = -3(1 + 4k) + -2 -2k + (7 * -7 + 3k * -7) = -3(1 + 4k) + -2 -2k + (-49 + -21k) = -3(1 + 4k) + -2 Reorder the terms: -49 + -2k + -21k = -3(1 + 4k) + -2 Combine like terms: -2k + -21k = -23k -49 + -23k = -3(1 + 4k) + -2 -49 + -23k = (1 * -3 + 4k * -3) + -2 -49 + -23k = (-3 + -12k) + -2 Reorder the terms: -49 + -23k = -3 + -2 + -12k Combine like terms: -3 + -2 = -5 -49 + -23k = -5 + -12k Solving -49 + -23k = -5 + -12k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '12k' to each side of the equation. -49 + -23k + 12k = -5 + -12k + 12k Combine like terms: -23k + 12k = -11k -49 + -11k = -5 + -12k + 12k Combine like terms: -12k + 12k = 0 -49 + -11k = -5 + 0 -49 + -11k = -5 Add '49' to each side of the equation. -49 + 49 + -11k = -5 + 49 Combine like terms: -49 + 49 = 0 0 + -11k = -5 + 49 -11k = -5 + 49 Combine like terms: -5 + 49 = 44 -11k = 44 Divide each side by '-11'. k = -4 Simplifying k = -4
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