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Simplifying 1 + 4k = -2(1 + -3k) * 7 Reorder the terms for easier multiplication: 1 + 4k = -2 * 7(1 + -3k) Multiply -2 * 7 1 + 4k = -14(1 + -3k) 1 + 4k = (1 * -14 + -3k * -14) 1 + 4k = (-14 + 42k) Solving 1 + 4k = -14 + 42k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-42k' to each side of the equation. 1 + 4k + -42k = -14 + 42k + -42k Combine like terms: 4k + -42k = -38k 1 + -38k = -14 + 42k + -42k Combine like terms: 42k + -42k = 0 1 + -38k = -14 + 0 1 + -38k = -14 Add '-1' to each side of the equation. 1 + -1 + -38k = -14 + -1 Combine like terms: 1 + -1 = 0 0 + -38k = -14 + -1 -38k = -14 + -1 Combine like terms: -14 + -1 = -15 -38k = -15 Divide each side by '-38'. k = 0.3947368421 Simplifying k = 0.3947368421
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