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Simplifying 7 + -7(6k + -7) = -10k + -12(4k + -10) Reorder the terms: 7 + -7(-7 + 6k) = -10k + -12(4k + -10) 7 + (-7 * -7 + 6k * -7) = -10k + -12(4k + -10) 7 + (49 + -42k) = -10k + -12(4k + -10) Combine like terms: 7 + 49 = 56 56 + -42k = -10k + -12(4k + -10) Reorder the terms: 56 + -42k = -10k + -12(-10 + 4k) 56 + -42k = -10k + (-10 * -12 + 4k * -12) 56 + -42k = -10k + (120 + -48k) Reorder the terms: 56 + -42k = 120 + -10k + -48k Combine like terms: -10k + -48k = -58k 56 + -42k = 120 + -58k Solving 56 + -42k = 120 + -58k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '58k' to each side of the equation. 56 + -42k + 58k = 120 + -58k + 58k Combine like terms: -42k + 58k = 16k 56 + 16k = 120 + -58k + 58k Combine like terms: -58k + 58k = 0 56 + 16k = 120 + 0 56 + 16k = 120 Add '-56' to each side of the equation. 56 + -56 + 16k = 120 + -56 Combine like terms: 56 + -56 = 0 0 + 16k = 120 + -56 16k = 120 + -56 Combine like terms: 120 + -56 = 64 16k = 64 Divide each side by '16'. k = 4 Simplifying k = 4
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