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Simplifying -6 = 3(k + 4) + -7(8 + -5k) Reorder the terms: -6 = 3(4 + k) + -7(8 + -5k) -6 = (4 * 3 + k * 3) + -7(8 + -5k) -6 = (12 + 3k) + -7(8 + -5k) -6 = 12 + 3k + (8 * -7 + -5k * -7) -6 = 12 + 3k + (-56 + 35k) Reorder the terms: -6 = 12 + -56 + 3k + 35k Combine like terms: 12 + -56 = -44 -6 = -44 + 3k + 35k Combine like terms: 3k + 35k = 38k -6 = -44 + 38k Solving -6 = -44 + 38k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-38k' to each side of the equation. -6 + -38k = -44 + 38k + -38k Combine like terms: 38k + -38k = 0 -6 + -38k = -44 + 0 -6 + -38k = -44 Add '6' to each side of the equation. -6 + 6 + -38k = -44 + 6 Combine like terms: -6 + 6 = 0 0 + -38k = -44 + 6 -38k = -44 + 6 Combine like terms: -44 + 6 = -38 -38k = -38 Divide each side by '-38'. k = 1 Simplifying k = 1
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