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Simplifying 75(24 + -20t) + 9t = 2(5t + 1) (24 * 75 + -20t * 75) + 9t = 2(5t + 1) (1800 + -1500t) + 9t = 2(5t + 1) Combine like terms: -1500t + 9t = -1491t 1800 + -1491t = 2(5t + 1) Reorder the terms: 1800 + -1491t = 2(1 + 5t) 1800 + -1491t = (1 * 2 + 5t * 2) 1800 + -1491t = (2 + 10t) Solving 1800 + -1491t = 2 + 10t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10t' to each side of the equation. 1800 + -1491t + -10t = 2 + 10t + -10t Combine like terms: -1491t + -10t = -1501t 1800 + -1501t = 2 + 10t + -10t Combine like terms: 10t + -10t = 0 1800 + -1501t = 2 + 0 1800 + -1501t = 2 Add '-1800' to each side of the equation. 1800 + -1800 + -1501t = 2 + -1800 Combine like terms: 1800 + -1800 = 0 0 + -1501t = 2 + -1800 -1501t = 2 + -1800 Combine like terms: 2 + -1800 = -1798 -1501t = -1798 Divide each side by '-1501'. t = 1.197868088 Simplifying t = 1.197868088
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