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Simplifying 2(4k + 1) + 3(2x + 3) = 0 Reorder the terms: 2(1 + 4k) + 3(2x + 3) = 0 (1 * 2 + 4k * 2) + 3(2x + 3) = 0 (2 + 8k) + 3(2x + 3) = 0 Reorder the terms: 2 + 8k + 3(3 + 2x) = 0 2 + 8k + (3 * 3 + 2x * 3) = 0 2 + 8k + (9 + 6x) = 0 Reorder the terms: 2 + 9 + 8k + 6x = 0 Combine like terms: 2 + 9 = 11 11 + 8k + 6x = 0 Solving 11 + 8k + 6x = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + 8k + -11 + 6x = 0 + -11 Reorder the terms: 11 + -11 + 8k + 6x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 8k + 6x = 0 + -11 8k + 6x = 0 + -11 Combine like terms: 0 + -11 = -11 8k + 6x = -11 Add '-6x' to each side of the equation. 8k + 6x + -6x = -11 + -6x Combine like terms: 6x + -6x = 0 8k + 0 = -11 + -6x 8k = -11 + -6x Divide each side by '8'. k = -1.375 + -0.75x Simplifying k = -1.375 + -0.75x
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