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Simplifying -7(4 + 6k) = -4(-10 + k) + -4k (4 * -7 + 6k * -7) = -4(-10 + k) + -4k (-28 + -42k) = -4(-10 + k) + -4k -28 + -42k = (-10 * -4 + k * -4) + -4k -28 + -42k = (40 + -4k) + -4k Combine like terms: -4k + -4k = -8k -28 + -42k = 40 + -8k Solving -28 + -42k = 40 + -8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '8k' to each side of the equation. -28 + -42k + 8k = 40 + -8k + 8k Combine like terms: -42k + 8k = -34k -28 + -34k = 40 + -8k + 8k Combine like terms: -8k + 8k = 0 -28 + -34k = 40 + 0 -28 + -34k = 40 Add '28' to each side of the equation. -28 + 28 + -34k = 40 + 28 Combine like terms: -28 + 28 = 0 0 + -34k = 40 + 28 -34k = 40 + 28 Combine like terms: 40 + 28 = 68 -34k = 68 Divide each side by '-34'. k = -2 Simplifying k = -2
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