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Simplifying 4(2t + 3) = 3(4t + 1) + -5(3t + -2) Reorder the terms: 4(3 + 2t) = 3(4t + 1) + -5(3t + -2) (3 * 4 + 2t * 4) = 3(4t + 1) + -5(3t + -2) (12 + 8t) = 3(4t + 1) + -5(3t + -2) Reorder the terms: 12 + 8t = 3(1 + 4t) + -5(3t + -2) 12 + 8t = (1 * 3 + 4t * 3) + -5(3t + -2) 12 + 8t = (3 + 12t) + -5(3t + -2) Reorder the terms: 12 + 8t = 3 + 12t + -5(-2 + 3t) 12 + 8t = 3 + 12t + (-2 * -5 + 3t * -5) 12 + 8t = 3 + 12t + (10 + -15t) Reorder the terms: 12 + 8t = 3 + 10 + 12t + -15t Combine like terms: 3 + 10 = 13 12 + 8t = 13 + 12t + -15t Combine like terms: 12t + -15t = -3t 12 + 8t = 13 + -3t Solving 12 + 8t = 13 + -3t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3t' to each side of the equation. 12 + 8t + 3t = 13 + -3t + 3t Combine like terms: 8t + 3t = 11t 12 + 11t = 13 + -3t + 3t Combine like terms: -3t + 3t = 0 12 + 11t = 13 + 0 12 + 11t = 13 Add '-12' to each side of the equation. 12 + -12 + 11t = 13 + -12 Combine like terms: 12 + -12 = 0 0 + 11t = 13 + -12 11t = 13 + -12 Combine like terms: 13 + -12 = 1 11t = 1 Divide each side by '11'. t = 0.09090909091 Simplifying t = 0.09090909091
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