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Simplifying 30 = -4(3 + 7k) + 7(-8 + -3k) 30 = (3 * -4 + 7k * -4) + 7(-8 + -3k) 30 = (-12 + -28k) + 7(-8 + -3k) 30 = -12 + -28k + (-8 * 7 + -3k * 7) 30 = -12 + -28k + (-56 + -21k) Reorder the terms: 30 = -12 + -56 + -28k + -21k Combine like terms: -12 + -56 = -68 30 = -68 + -28k + -21k Combine like terms: -28k + -21k = -49k 30 = -68 + -49k Solving 30 = -68 + -49k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '49k' to each side of the equation. 30 + 49k = -68 + -49k + 49k Combine like terms: -49k + 49k = 0 30 + 49k = -68 + 0 30 + 49k = -68 Add '-30' to each side of the equation. 30 + -30 + 49k = -68 + -30 Combine like terms: 30 + -30 = 0 0 + 49k = -68 + -30 49k = -68 + -30 Combine like terms: -68 + -30 = -98 49k = -98 Divide each side by '49'. k = -2 Simplifying k = -2
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