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Simplifying 5(t + 2) + -1(4t + -5) = 3(2t + 4) + -2 Reorder the terms: 5(2 + t) + -1(4t + -5) = 3(2t + 4) + -2 (2 * 5 + t * 5) + -1(4t + -5) = 3(2t + 4) + -2 (10 + 5t) + -1(4t + -5) = 3(2t + 4) + -2 Reorder the terms: 10 + 5t + -1(-5 + 4t) = 3(2t + 4) + -2 10 + 5t + (-5 * -1 + 4t * -1) = 3(2t + 4) + -2 10 + 5t + (5 + -4t) = 3(2t + 4) + -2 Reorder the terms: 10 + 5 + 5t + -4t = 3(2t + 4) + -2 Combine like terms: 10 + 5 = 15 15 + 5t + -4t = 3(2t + 4) + -2 Combine like terms: 5t + -4t = 1t 15 + 1t = 3(2t + 4) + -2 Reorder the terms: 15 + 1t = 3(4 + 2t) + -2 15 + 1t = (4 * 3 + 2t * 3) + -2 15 + 1t = (12 + 6t) + -2 Reorder the terms: 15 + 1t = 12 + -2 + 6t Combine like terms: 12 + -2 = 10 15 + 1t = 10 + 6t Solving 15 + 1t = 10 + 6t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6t' to each side of the equation. 15 + 1t + -6t = 10 + 6t + -6t Combine like terms: 1t + -6t = -5t 15 + -5t = 10 + 6t + -6t Combine like terms: 6t + -6t = 0 15 + -5t = 10 + 0 15 + -5t = 10 Add '-15' to each side of the equation. 15 + -15 + -5t = 10 + -15 Combine like terms: 15 + -15 = 0 0 + -5t = 10 + -15 -5t = 10 + -15 Combine like terms: 10 + -15 = -5 -5t = -5 Divide each side by '-5'. t = 1 Simplifying t = 1
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