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Simplifying -4(3 + -4k) = 7k + 42 (3 * -4 + -4k * -4) = 7k + 42 (-12 + 16k) = 7k + 42 Reorder the terms: -12 + 16k = 42 + 7k Solving -12 + 16k = 42 + 7k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7k' to each side of the equation. -12 + 16k + -7k = 42 + 7k + -7k Combine like terms: 16k + -7k = 9k -12 + 9k = 42 + 7k + -7k Combine like terms: 7k + -7k = 0 -12 + 9k = 42 + 0 -12 + 9k = 42 Add '12' to each side of the equation. -12 + 12 + 9k = 42 + 12 Combine like terms: -12 + 12 = 0 0 + 9k = 42 + 12 9k = 42 + 12 Combine like terms: 42 + 12 = 54 9k = 54 Divide each side by '9'. k = 6 Simplifying k = 6
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