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Simplifying -4(k + 4) + 13(k + -1) = -3(k + -2) + 7 Reorder the terms: -4(4 + k) + 13(k + -1) = -3(k + -2) + 7 (4 * -4 + k * -4) + 13(k + -1) = -3(k + -2) + 7 (-16 + -4k) + 13(k + -1) = -3(k + -2) + 7 Reorder the terms: -16 + -4k + 13(-1 + k) = -3(k + -2) + 7 -16 + -4k + (-1 * 13 + k * 13) = -3(k + -2) + 7 -16 + -4k + (-13 + 13k) = -3(k + -2) + 7 Reorder the terms: -16 + -13 + -4k + 13k = -3(k + -2) + 7 Combine like terms: -16 + -13 = -29 -29 + -4k + 13k = -3(k + -2) + 7 Combine like terms: -4k + 13k = 9k -29 + 9k = -3(k + -2) + 7 Reorder the terms: -29 + 9k = -3(-2 + k) + 7 -29 + 9k = (-2 * -3 + k * -3) + 7 -29 + 9k = (6 + -3k) + 7 Reorder the terms: -29 + 9k = 6 + 7 + -3k Combine like terms: 6 + 7 = 13 -29 + 9k = 13 + -3k Solving -29 + 9k = 13 + -3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3k' to each side of the equation. -29 + 9k + 3k = 13 + -3k + 3k Combine like terms: 9k + 3k = 12k -29 + 12k = 13 + -3k + 3k Combine like terms: -3k + 3k = 0 -29 + 12k = 13 + 0 -29 + 12k = 13 Add '29' to each side of the equation. -29 + 29 + 12k = 13 + 29 Combine like terms: -29 + 29 = 0 0 + 12k = 13 + 29 12k = 13 + 29 Combine like terms: 13 + 29 = 42 12k = 42 Divide each side by '12'. k = 3.5 Simplifying k = 3.5
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