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Simplifying 5(-4k + -6) + -1 = 7k + -31 Reorder the terms: 5(-6 + -4k) + -1 = 7k + -31 (-6 * 5 + -4k * 5) + -1 = 7k + -31 (-30 + -20k) + -1 = 7k + -31 Reorder the terms: -30 + -1 + -20k = 7k + -31 Combine like terms: -30 + -1 = -31 -31 + -20k = 7k + -31 Reorder the terms: -31 + -20k = -31 + 7k Add '31' to each side of the equation. -31 + 31 + -20k = -31 + 31 + 7k Combine like terms: -31 + 31 = 0 0 + -20k = -31 + 31 + 7k -20k = -31 + 31 + 7k Combine like terms: -31 + 31 = 0 -20k = 0 + 7k -20k = 7k Solving -20k = 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. -20k + -7k = 7k + -7k Combine like terms: -20k + -7k = -27k -27k = 7k + -7k Combine like terms: 7k + -7k = 0 -27k = 0 Divide each side by '-27'. k = 0 Simplifying k = 0
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