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Simplifying (7 + 9t)(-2) + 3(-5 + 4k) = 0 Reorder the terms for easier multiplication: -2(7 + 9t) + 3(-5 + 4k) = 0 (7 * -2 + 9t * -2) + 3(-5 + 4k) = 0 (-14 + -18t) + 3(-5 + 4k) = 0 -14 + -18t + (-5 * 3 + 4k * 3) = 0 -14 + -18t + (-15 + 12k) = 0 Reorder the terms: -14 + -15 + 12k + -18t = 0 Combine like terms: -14 + -15 = -29 -29 + 12k + -18t = 0 Solving -29 + 12k + -18t = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 12k + 29 + -18t = 0 + 29 Reorder the terms: -29 + 29 + 12k + -18t = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 12k + -18t = 0 + 29 12k + -18t = 0 + 29 Combine like terms: 0 + 29 = 29 12k + -18t = 29 Add '18t' to each side of the equation. 12k + -18t + 18t = 29 + 18t Combine like terms: -18t + 18t = 0 12k + 0 = 29 + 18t 12k = 29 + 18t Divide each side by '12'. k = 2.416666667 + 1.5t Simplifying k = 2.416666667 + 1.5t
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