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Simplifying -2(1 + 4k) = -2 + -4(k + -8) (1 * -2 + 4k * -2) = -2 + -4(k + -8) (-2 + -8k) = -2 + -4(k + -8) Reorder the terms: -2 + -8k = -2 + -4(-8 + k) -2 + -8k = -2 + (-8 * -4 + k * -4) -2 + -8k = -2 + (32 + -4k) Combine like terms: -2 + 32 = 30 -2 + -8k = 30 + -4k Solving -2 + -8k = 30 + -4k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4k' to each side of the equation. -2 + -8k + 4k = 30 + -4k + 4k Combine like terms: -8k + 4k = -4k -2 + -4k = 30 + -4k + 4k Combine like terms: -4k + 4k = 0 -2 + -4k = 30 + 0 -2 + -4k = 30 Add '2' to each side of the equation. -2 + 2 + -4k = 30 + 2 Combine like terms: -2 + 2 = 0 0 + -4k = 30 + 2 -4k = 30 + 2 Combine like terms: 30 + 2 = 32 -4k = 32 Divide each side by '-4'. k = -8 Simplifying k = -8
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