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Simplifying 2(t + -4) + -3(4t + -5) = 10 + -5(7t + 3) Reorder the terms: 2(-4 + t) + -3(4t + -5) = 10 + -5(7t + 3) (-4 * 2 + t * 2) + -3(4t + -5) = 10 + -5(7t + 3) (-8 + 2t) + -3(4t + -5) = 10 + -5(7t + 3) Reorder the terms: -8 + 2t + -3(-5 + 4t) = 10 + -5(7t + 3) -8 + 2t + (-5 * -3 + 4t * -3) = 10 + -5(7t + 3) -8 + 2t + (15 + -12t) = 10 + -5(7t + 3) Reorder the terms: -8 + 15 + 2t + -12t = 10 + -5(7t + 3) Combine like terms: -8 + 15 = 7 7 + 2t + -12t = 10 + -5(7t + 3) Combine like terms: 2t + -12t = -10t 7 + -10t = 10 + -5(7t + 3) Reorder the terms: 7 + -10t = 10 + -5(3 + 7t) 7 + -10t = 10 + (3 * -5 + 7t * -5) 7 + -10t = 10 + (-15 + -35t) Combine like terms: 10 + -15 = -5 7 + -10t = -5 + -35t Solving 7 + -10t = -5 + -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. 7 + -10t + 35t = -5 + -35t + 35t Combine like terms: -10t + 35t = 25t 7 + 25t = -5 + -35t + 35t Combine like terms: -35t + 35t = 0 7 + 25t = -5 + 0 7 + 25t = -5 Add '-7' to each side of the equation. 7 + -7 + 25t = -5 + -7 Combine like terms: 7 + -7 = 0 0 + 25t = -5 + -7 25t = -5 + -7 Combine like terms: -5 + -7 = -12 25t = -12 Divide each side by '25'. t = -0.48 Simplifying t = -0.48
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