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Simplifying -6(w + -4) + -7k = 32 + -2(k + 8) Reorder the terms: -6(-4 + w) + -7k = 32 + -2(k + 8) (-4 * -6 + w * -6) + -7k = 32 + -2(k + 8) (24 + -6w) + -7k = 32 + -2(k + 8) Reorder the terms: 24 + -7k + -6w = 32 + -2(k + 8) Reorder the terms: 24 + -7k + -6w = 32 + -2(8 + k) 24 + -7k + -6w = 32 + (8 * -2 + k * -2) 24 + -7k + -6w = 32 + (-16 + -2k) Combine like terms: 32 + -16 = 16 24 + -7k + -6w = 16 + -2k Solving 24 + -7k + -6w = 16 + -2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2k' to each side of the equation. 24 + -7k + 2k + -6w = 16 + -2k + 2k Combine like terms: -7k + 2k = -5k 24 + -5k + -6w = 16 + -2k + 2k Combine like terms: -2k + 2k = 0 24 + -5k + -6w = 16 + 0 24 + -5k + -6w = 16 Add '-24' to each side of the equation. 24 + -5k + -24 + -6w = 16 + -24 Reorder the terms: 24 + -24 + -5k + -6w = 16 + -24 Combine like terms: 24 + -24 = 0 0 + -5k + -6w = 16 + -24 -5k + -6w = 16 + -24 Combine like terms: 16 + -24 = -8 -5k + -6w = -8 Add '6w' to each side of the equation. -5k + -6w + 6w = -8 + 6w Combine like terms: -6w + 6w = 0 -5k + 0 = -8 + 6w -5k = -8 + 6w Divide each side by '-5'. k = 1.6 + -1.2w Simplifying k = 1.6 + -1.2w
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