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Simplifying 5(t + 1) + -2(8t + 5) = -12(t + -1) + -5 Reorder the terms: 5(1 + t) + -2(8t + 5) = -12(t + -1) + -5 (1 * 5 + t * 5) + -2(8t + 5) = -12(t + -1) + -5 (5 + 5t) + -2(8t + 5) = -12(t + -1) + -5 Reorder the terms: 5 + 5t + -2(5 + 8t) = -12(t + -1) + -5 5 + 5t + (5 * -2 + 8t * -2) = -12(t + -1) + -5 5 + 5t + (-10 + -16t) = -12(t + -1) + -5 Reorder the terms: 5 + -10 + 5t + -16t = -12(t + -1) + -5 Combine like terms: 5 + -10 = -5 -5 + 5t + -16t = -12(t + -1) + -5 Combine like terms: 5t + -16t = -11t -5 + -11t = -12(t + -1) + -5 Reorder the terms: -5 + -11t = -12(-1 + t) + -5 -5 + -11t = (-1 * -12 + t * -12) + -5 -5 + -11t = (12 + -12t) + -5 Reorder the terms: -5 + -11t = 12 + -5 + -12t Combine like terms: 12 + -5 = 7 -5 + -11t = 7 + -12t Solving -5 + -11t = 7 + -12t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12t' to each side of the equation. -5 + -11t + 12t = 7 + -12t + 12t Combine like terms: -11t + 12t = 1t -5 + 1t = 7 + -12t + 12t Combine like terms: -12t + 12t = 0 -5 + 1t = 7 + 0 -5 + 1t = 7 Add '5' to each side of the equation. -5 + 5 + 1t = 7 + 5 Combine like terms: -5 + 5 = 0 0 + 1t = 7 + 5 1t = 7 + 5 Combine like terms: 7 + 5 = 12 1t = 12 Divide each side by '1'. t = 12 Simplifying t = 12
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