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Simplifying 5(3 + -2k) = 8(3k + -4) + -4(1 + 7k) (3 * 5 + -2k * 5) = 8(3k + -4) + -4(1 + 7k) (15 + -10k) = 8(3k + -4) + -4(1 + 7k) Reorder the terms: 15 + -10k = 8(-4 + 3k) + -4(1 + 7k) 15 + -10k = (-4 * 8 + 3k * 8) + -4(1 + 7k) 15 + -10k = (-32 + 24k) + -4(1 + 7k) 15 + -10k = -32 + 24k + (1 * -4 + 7k * -4) 15 + -10k = -32 + 24k + (-4 + -28k) Reorder the terms: 15 + -10k = -32 + -4 + 24k + -28k Combine like terms: -32 + -4 = -36 15 + -10k = -36 + 24k + -28k Combine like terms: 24k + -28k = -4k 15 + -10k = -36 + -4k Solving 15 + -10k = -36 + -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. 15 + -10k + 4k = -36 + -4k + 4k Combine like terms: -10k + 4k = -6k 15 + -6k = -36 + -4k + 4k Combine like terms: -4k + 4k = 0 15 + -6k = -36 + 0 15 + -6k = -36 Add '-15' to each side of the equation. 15 + -15 + -6k = -36 + -15 Combine like terms: 15 + -15 = 0 0 + -6k = -36 + -15 -6k = -36 + -15 Combine like terms: -36 + -15 = -51 -6k = -51 Divide each side by '-6'. k = 8.5 Simplifying k = 8.5
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