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Simplifying 5(2k + 1) = 6(3k + -4) + 7 Reorder the terms: 5(1 + 2k) = 6(3k + -4) + 7 (1 * 5 + 2k * 5) = 6(3k + -4) + 7 (5 + 10k) = 6(3k + -4) + 7 Reorder the terms: 5 + 10k = 6(-4 + 3k) + 7 5 + 10k = (-4 * 6 + 3k * 6) + 7 5 + 10k = (-24 + 18k) + 7 Reorder the terms: 5 + 10k = -24 + 7 + 18k Combine like terms: -24 + 7 = -17 5 + 10k = -17 + 18k Solving 5 + 10k = -17 + 18k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-18k' to each side of the equation. 5 + 10k + -18k = -17 + 18k + -18k Combine like terms: 10k + -18k = -8k 5 + -8k = -17 + 18k + -18k Combine like terms: 18k + -18k = 0 5 + -8k = -17 + 0 5 + -8k = -17 Add '-5' to each side of the equation. 5 + -5 + -8k = -17 + -5 Combine like terms: 5 + -5 = 0 0 + -8k = -17 + -5 -8k = -17 + -5 Combine like terms: -17 + -5 = -22 -8k = -22 Divide each side by '-8'. k = 2.75 Simplifying k = 2.75
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