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Simplifying -3(1 + 31k) + -30k = -4(29k + 13) (1 * -3 + 31k * -3) + -30k = -4(29k + 13) (-3 + -93k) + -30k = -4(29k + 13) Combine like terms: -93k + -30k = -123k -3 + -123k = -4(29k + 13) Reorder the terms: -3 + -123k = -4(13 + 29k) -3 + -123k = (13 * -4 + 29k * -4) -3 + -123k = (-52 + -116k) Solving -3 + -123k = -52 + -116k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '116k' to each side of the equation. -3 + -123k + 116k = -52 + -116k + 116k Combine like terms: -123k + 116k = -7k -3 + -7k = -52 + -116k + 116k Combine like terms: -116k + 116k = 0 -3 + -7k = -52 + 0 -3 + -7k = -52 Add '3' to each side of the equation. -3 + 3 + -7k = -52 + 3 Combine like terms: -3 + 3 = 0 0 + -7k = -52 + 3 -7k = -52 + 3 Combine like terms: -52 + 3 = -49 -7k = -49 Divide each side by '-7'. k = 7 Simplifying k = 7
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