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Simplifying 1 + -4k + -6 + 3k = -7(k + -1) + -12(1 + -9k) Reorder the terms: 1 + -6 + -4k + 3k = -7(k + -1) + -12(1 + -9k) Combine like terms: 1 + -6 = -5 -5 + -4k + 3k = -7(k + -1) + -12(1 + -9k) Combine like terms: -4k + 3k = -1k -5 + -1k = -7(k + -1) + -12(1 + -9k) Reorder the terms: -5 + -1k = -7(-1 + k) + -12(1 + -9k) -5 + -1k = (-1 * -7 + k * -7) + -12(1 + -9k) -5 + -1k = (7 + -7k) + -12(1 + -9k) -5 + -1k = 7 + -7k + (1 * -12 + -9k * -12) -5 + -1k = 7 + -7k + (-12 + 108k) Reorder the terms: -5 + -1k = 7 + -12 + -7k + 108k Combine like terms: 7 + -12 = -5 -5 + -1k = -5 + -7k + 108k Combine like terms: -7k + 108k = 101k -5 + -1k = -5 + 101k Add '5' to each side of the equation. -5 + 5 + -1k = -5 + 5 + 101k Combine like terms: -5 + 5 = 0 0 + -1k = -5 + 5 + 101k -1k = -5 + 5 + 101k Combine like terms: -5 + 5 = 0 -1k = 0 + 101k -1k = 101k Solving -1k = 101k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-101k' to each side of the equation. -1k + -101k = 101k + -101k Combine like terms: -1k + -101k = -102k -102k = 101k + -101k Combine like terms: 101k + -101k = 0 -102k = 0 Divide each side by '-102'. k = 0 Simplifying k = 0
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