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Simplifying 5(t + 3) + 4 = 3(t + -2) + 1 Reorder the terms: 5(3 + t) + 4 = 3(t + -2) + 1 (3 * 5 + t * 5) + 4 = 3(t + -2) + 1 (15 + 5t) + 4 = 3(t + -2) + 1 Reorder the terms: 15 + 4 + 5t = 3(t + -2) + 1 Combine like terms: 15 + 4 = 19 19 + 5t = 3(t + -2) + 1 Reorder the terms: 19 + 5t = 3(-2 + t) + 1 19 + 5t = (-2 * 3 + t * 3) + 1 19 + 5t = (-6 + 3t) + 1 Reorder the terms: 19 + 5t = -6 + 1 + 3t Combine like terms: -6 + 1 = -5 19 + 5t = -5 + 3t Solving 19 + 5t = -5 + 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. 19 + 5t + -3t = -5 + 3t + -3t Combine like terms: 5t + -3t = 2t 19 + 2t = -5 + 3t + -3t Combine like terms: 3t + -3t = 0 19 + 2t = -5 + 0 19 + 2t = -5 Add '-19' to each side of the equation. 19 + -19 + 2t = -5 + -19 Combine like terms: 19 + -19 = 0 0 + 2t = -5 + -19 2t = -5 + -19 Combine like terms: -5 + -19 = -24 2t = -24 Divide each side by '2'. t = -12 Simplifying t = -12
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