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Simplifying -2[3k + 3(k + -8)] = -2[3(k + 7)] Reorder the terms: -2[3k + 3(-8 + k)] = -2[3(k + 7)] -2[3k + (-8 * 3 + k * 3)] = -2[3(k + 7)] -2[3k + (-24 + 3k)] = -2[3(k + 7)] Reorder the terms: -2[-24 + 3k + 3k] = -2[3(k + 7)] Combine like terms: 3k + 3k = 6k -2[-24 + 6k] = -2[3(k + 7)] [-24 * -2 + 6k * -2] = -2[3(k + 7)] [48 + -12k] = -2[3(k + 7)] Reorder the terms: 48 + -12k = -2[3(7 + k)] 48 + -12k = -2[(7 * 3 + k * 3)] 48 + -12k = -2[(21 + 3k)] 48 + -12k = [21 * -2 + 3k * -2] 48 + -12k = [-42 + -6k] Solving 48 + -12k = -42 + -6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '6k' to each side of the equation. 48 + -12k + 6k = -42 + -6k + 6k Combine like terms: -12k + 6k = -6k 48 + -6k = -42 + -6k + 6k Combine like terms: -6k + 6k = 0 48 + -6k = -42 + 0 48 + -6k = -42 Add '-48' to each side of the equation. 48 + -48 + -6k = -42 + -48 Combine like terms: 48 + -48 = 0 0 + -6k = -42 + -48 -6k = -42 + -48 Combine like terms: -42 + -48 = -90 -6k = -90 Divide each side by '-6'. k = 15 Simplifying k = 15
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