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Simplifying 4(-1t + 3) + 6(2t + 6) = t + 4 + -5t Reorder the terms: 4(3 + -1t) + 6(2t + 6) = t + 4 + -5t (3 * 4 + -1t * 4) + 6(2t + 6) = t + 4 + -5t (12 + -4t) + 6(2t + 6) = t + 4 + -5t Reorder the terms: 12 + -4t + 6(6 + 2t) = t + 4 + -5t 12 + -4t + (6 * 6 + 2t * 6) = t + 4 + -5t 12 + -4t + (36 + 12t) = t + 4 + -5t Reorder the terms: 12 + 36 + -4t + 12t = t + 4 + -5t Combine like terms: 12 + 36 = 48 48 + -4t + 12t = t + 4 + -5t Combine like terms: -4t + 12t = 8t 48 + 8t = t + 4 + -5t Reorder the terms: 48 + 8t = 4 + t + -5t Combine like terms: t + -5t = -4t 48 + 8t = 4 + -4t Solving 48 + 8t = 4 + -4t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4t' to each side of the equation. 48 + 8t + 4t = 4 + -4t + 4t Combine like terms: 8t + 4t = 12t 48 + 12t = 4 + -4t + 4t Combine like terms: -4t + 4t = 0 48 + 12t = 4 + 0 48 + 12t = 4 Add '-48' to each side of the equation. 48 + -48 + 12t = 4 + -48 Combine like terms: 48 + -48 = 0 0 + 12t = 4 + -48 12t = 4 + -48 Combine like terms: 4 + -48 = -44 12t = -44 Divide each side by '12'. t = -3.666666667 Simplifying t = -3.666666667
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