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Simplifying -6k + 4(1 + -4k) = 2 + -4(6k + -7) -6k + (1 * 4 + -4k * 4) = 2 + -4(6k + -7) -6k + (4 + -16k) = 2 + -4(6k + -7) Reorder the terms: 4 + -6k + -16k = 2 + -4(6k + -7) Combine like terms: -6k + -16k = -22k 4 + -22k = 2 + -4(6k + -7) Reorder the terms: 4 + -22k = 2 + -4(-7 + 6k) 4 + -22k = 2 + (-7 * -4 + 6k * -4) 4 + -22k = 2 + (28 + -24k) Combine like terms: 2 + 28 = 30 4 + -22k = 30 + -24k Solving 4 + -22k = 30 + -24k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '24k' to each side of the equation. 4 + -22k + 24k = 30 + -24k + 24k Combine like terms: -22k + 24k = 2k 4 + 2k = 30 + -24k + 24k Combine like terms: -24k + 24k = 0 4 + 2k = 30 + 0 4 + 2k = 30 Add '-4' to each side of the equation. 4 + -4 + 2k = 30 + -4 Combine like terms: 4 + -4 = 0 0 + 2k = 30 + -4 2k = 30 + -4 Combine like terms: 30 + -4 = 26 2k = 26 Divide each side by '2'. k = 13 Simplifying k = 13
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