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Simplifying -9(t + -2) + 7(1 + -5t) = -45(t + -1) + -2 Reorder the terms: -9(-2 + t) + 7(1 + -5t) = -45(t + -1) + -2 (-2 * -9 + t * -9) + 7(1 + -5t) = -45(t + -1) + -2 (18 + -9t) + 7(1 + -5t) = -45(t + -1) + -2 18 + -9t + (1 * 7 + -5t * 7) = -45(t + -1) + -2 18 + -9t + (7 + -35t) = -45(t + -1) + -2 Reorder the terms: 18 + 7 + -9t + -35t = -45(t + -1) + -2 Combine like terms: 18 + 7 = 25 25 + -9t + -35t = -45(t + -1) + -2 Combine like terms: -9t + -35t = -44t 25 + -44t = -45(t + -1) + -2 Reorder the terms: 25 + -44t = -45(-1 + t) + -2 25 + -44t = (-1 * -45 + t * -45) + -2 25 + -44t = (45 + -45t) + -2 Reorder the terms: 25 + -44t = 45 + -2 + -45t Combine like terms: 45 + -2 = 43 25 + -44t = 43 + -45t Solving 25 + -44t = 43 + -45t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '45t' to each side of the equation. 25 + -44t + 45t = 43 + -45t + 45t Combine like terms: -44t + 45t = 1t 25 + 1t = 43 + -45t + 45t Combine like terms: -45t + 45t = 0 25 + 1t = 43 + 0 25 + 1t = 43 Add '-25' to each side of the equation. 25 + -25 + 1t = 43 + -25 Combine like terms: 25 + -25 = 0 0 + 1t = 43 + -25 1t = 43 + -25 Combine like terms: 43 + -25 = 18 1t = 18 Divide each side by '1'. t = 18 Simplifying t = 18
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