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Simplifying -9(t + -8) + -5(-6t + -3) = 20(t + 5) + 9 Reorder the terms: -9(-8 + t) + -5(-6t + -3) = 20(t + 5) + 9 (-8 * -9 + t * -9) + -5(-6t + -3) = 20(t + 5) + 9 (72 + -9t) + -5(-6t + -3) = 20(t + 5) + 9 Reorder the terms: 72 + -9t + -5(-3 + -6t) = 20(t + 5) + 9 72 + -9t + (-3 * -5 + -6t * -5) = 20(t + 5) + 9 72 + -9t + (15 + 30t) = 20(t + 5) + 9 Reorder the terms: 72 + 15 + -9t + 30t = 20(t + 5) + 9 Combine like terms: 72 + 15 = 87 87 + -9t + 30t = 20(t + 5) + 9 Combine like terms: -9t + 30t = 21t 87 + 21t = 20(t + 5) + 9 Reorder the terms: 87 + 21t = 20(5 + t) + 9 87 + 21t = (5 * 20 + t * 20) + 9 87 + 21t = (100 + 20t) + 9 Reorder the terms: 87 + 21t = 100 + 9 + 20t Combine like terms: 100 + 9 = 109 87 + 21t = 109 + 20t Solving 87 + 21t = 109 + 20t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20t' to each side of the equation. 87 + 21t + -20t = 109 + 20t + -20t Combine like terms: 21t + -20t = 1t 87 + 1t = 109 + 20t + -20t Combine like terms: 20t + -20t = 0 87 + 1t = 109 + 0 87 + 1t = 109 Add '-87' to each side of the equation. 87 + -87 + 1t = 109 + -87 Combine like terms: 87 + -87 = 0 0 + 1t = 109 + -87 1t = 109 + -87 Combine like terms: 109 + -87 = 22 1t = 22 Divide each side by '1'. t = 22 Simplifying t = 22
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