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Simplifying 2(t + -3) + -3(4t + -3) = 2 + -5(7t + 1) Reorder the terms: 2(-3 + t) + -3(4t + -3) = 2 + -5(7t + 1) (-3 * 2 + t * 2) + -3(4t + -3) = 2 + -5(7t + 1) (-6 + 2t) + -3(4t + -3) = 2 + -5(7t + 1) Reorder the terms: -6 + 2t + -3(-3 + 4t) = 2 + -5(7t + 1) -6 + 2t + (-3 * -3 + 4t * -3) = 2 + -5(7t + 1) -6 + 2t + (9 + -12t) = 2 + -5(7t + 1) Reorder the terms: -6 + 9 + 2t + -12t = 2 + -5(7t + 1) Combine like terms: -6 + 9 = 3 3 + 2t + -12t = 2 + -5(7t + 1) Combine like terms: 2t + -12t = -10t 3 + -10t = 2 + -5(7t + 1) Reorder the terms: 3 + -10t = 2 + -5(1 + 7t) 3 + -10t = 2 + (1 * -5 + 7t * -5) 3 + -10t = 2 + (-5 + -35t) Combine like terms: 2 + -5 = -3 3 + -10t = -3 + -35t Solving 3 + -10t = -3 + -35t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35t' to each side of the equation. 3 + -10t + 35t = -3 + -35t + 35t Combine like terms: -10t + 35t = 25t 3 + 25t = -3 + -35t + 35t Combine like terms: -35t + 35t = 0 3 + 25t = -3 + 0 3 + 25t = -3 Add '-3' to each side of the equation. 3 + -3 + 25t = -3 + -3 Combine like terms: 3 + -3 = 0 0 + 25t = -3 + -3 25t = -3 + -3 Combine like terms: -3 + -3 = -6 25t = -6 Divide each side by '25'. t = -0.24 Simplifying t = -0.24
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