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Simplifying 8(4k + 1) = 15k + 6(10k + -13) Reorder the terms: 8(1 + 4k) = 15k + 6(10k + -13) (1 * 8 + 4k * 8) = 15k + 6(10k + -13) (8 + 32k) = 15k + 6(10k + -13) Reorder the terms: 8 + 32k = 15k + 6(-13 + 10k) 8 + 32k = 15k + (-13 * 6 + 10k * 6) 8 + 32k = 15k + (-78 + 60k) Reorder the terms: 8 + 32k = -78 + 15k + 60k Combine like terms: 15k + 60k = 75k 8 + 32k = -78 + 75k Solving 8 + 32k = -78 + 75k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-75k' to each side of the equation. 8 + 32k + -75k = -78 + 75k + -75k Combine like terms: 32k + -75k = -43k 8 + -43k = -78 + 75k + -75k Combine like terms: 75k + -75k = 0 8 + -43k = -78 + 0 8 + -43k = -78 Add '-8' to each side of the equation. 8 + -8 + -43k = -78 + -8 Combine like terms: 8 + -8 = 0 0 + -43k = -78 + -8 -43k = -78 + -8 Combine like terms: -78 + -8 = -86 -43k = -86 Divide each side by '-43'. k = 2 Simplifying k = 2
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