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Simplifying 3(t + 1) + -5(3t + 3) = -13(t + 2) + -9 Reorder the terms: 3(1 + t) + -5(3t + 3) = -13(t + 2) + -9 (1 * 3 + t * 3) + -5(3t + 3) = -13(t + 2) + -9 (3 + 3t) + -5(3t + 3) = -13(t + 2) + -9 Reorder the terms: 3 + 3t + -5(3 + 3t) = -13(t + 2) + -9 3 + 3t + (3 * -5 + 3t * -5) = -13(t + 2) + -9 3 + 3t + (-15 + -15t) = -13(t + 2) + -9 Reorder the terms: 3 + -15 + 3t + -15t = -13(t + 2) + -9 Combine like terms: 3 + -15 = -12 -12 + 3t + -15t = -13(t + 2) + -9 Combine like terms: 3t + -15t = -12t -12 + -12t = -13(t + 2) + -9 Reorder the terms: -12 + -12t = -13(2 + t) + -9 -12 + -12t = (2 * -13 + t * -13) + -9 -12 + -12t = (-26 + -13t) + -9 Reorder the terms: -12 + -12t = -26 + -9 + -13t Combine like terms: -26 + -9 = -35 -12 + -12t = -35 + -13t Solving -12 + -12t = -35 + -13t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13t' to each side of the equation. -12 + -12t + 13t = -35 + -13t + 13t Combine like terms: -12t + 13t = 1t -12 + 1t = -35 + -13t + 13t Combine like terms: -13t + 13t = 0 -12 + 1t = -35 + 0 -12 + 1t = -35 Add '12' to each side of the equation. -12 + 12 + 1t = -35 + 12 Combine like terms: -12 + 12 = 0 0 + 1t = -35 + 12 1t = -35 + 12 Combine like terms: -35 + 12 = -23 1t = -23 Divide each side by '1'. t = -23 Simplifying t = -23
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