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Simplifying -3(1 + 9k) + -7(-12k + 1) = 1 + 0k + -11 + -6k (1 * -3 + 9k * -3) + -7(-12k + 1) = 1 + 0k + -11 + -6k (-3 + -27k) + -7(-12k + 1) = 1 + 0k + -11 + -6k Reorder the terms: -3 + -27k + -7(1 + -12k) = 1 + 0k + -11 + -6k -3 + -27k + (1 * -7 + -12k * -7) = 1 + 0k + -11 + -6k -3 + -27k + (-7 + 84k) = 1 + 0k + -11 + -6k Reorder the terms: -3 + -7 + -27k + 84k = 1 + 0k + -11 + -6k Combine like terms: -3 + -7 = -10 -10 + -27k + 84k = 1 + 0k + -11 + -6k Combine like terms: -27k + 84k = 57k -10 + 57k = 1 + 0k + -11 + -6k Anything times zero is zero. -10 + 57k = 1 + 0k + -11 + -6k Combine like terms: 1 + 0 = 1 -10 + 57k = 1 + -11 + -6k Combine like terms: 1 + -11 = -10 -10 + 57k = -10 + -6k Add '10' to each side of the equation. -10 + 10 + 57k = -10 + 10 + -6k Combine like terms: -10 + 10 = 0 0 + 57k = -10 + 10 + -6k 57k = -10 + 10 + -6k Combine like terms: -10 + 10 = 0 57k = 0 + -6k 57k = -6k Solving 57k = -6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '6k' to each side of the equation. 57k + 6k = -6k + 6k Combine like terms: 57k + 6k = 63k 63k = -6k + 6k Combine like terms: -6k + 6k = 0 63k = 0 Divide each side by '63'. k = 0 Simplifying k = 0
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