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Simplifying -6(4k + 6) + 3 = 6(1 + 3k) + 3 Reorder the terms: -6(6 + 4k) + 3 = 6(1 + 3k) + 3 (6 * -6 + 4k * -6) + 3 = 6(1 + 3k) + 3 (-36 + -24k) + 3 = 6(1 + 3k) + 3 Reorder the terms: -36 + 3 + -24k = 6(1 + 3k) + 3 Combine like terms: -36 + 3 = -33 -33 + -24k = 6(1 + 3k) + 3 -33 + -24k = (1 * 6 + 3k * 6) + 3 -33 + -24k = (6 + 18k) + 3 Reorder the terms: -33 + -24k = 6 + 3 + 18k Combine like terms: 6 + 3 = 9 -33 + -24k = 9 + 18k Solving -33 + -24k = 9 + 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. -33 + -24k + -18k = 9 + 18k + -18k Combine like terms: -24k + -18k = -42k -33 + -42k = 9 + 18k + -18k Combine like terms: 18k + -18k = 0 -33 + -42k = 9 + 0 -33 + -42k = 9 Add '33' to each side of the equation. -33 + 33 + -42k = 9 + 33 Combine like terms: -33 + 33 = 0 0 + -42k = 9 + 33 -42k = 9 + 33 Combine like terms: 9 + 33 = 42 -42k = 42 Divide each side by '-42'. k = -1 Simplifying k = -1
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