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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 = -23k 12 + -23k = 42 + 7k + -7k Combine like terms: 7k + -7k = 0 12 + -23k = 42 + 0 12 + -23k = 42 Add '-12' to each side of the equation. 12 + -12 + -23k = 42 + -12 Combine like terms: 12 + -12 = 0 0 + -23k = 42 + -12 -23k = 42 + -12 Combine like terms: 42 + -12 = 30 -23k = 30 Divide each side by '-23'. k = -1.304347826 Simplifying k = -1.304347826
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