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Simplifying 2(t + -1) + -3(4t + -3) = 10 + -5(5t + 1) Reorder the terms: 2(-1 + t) + -3(4t + -3) = 10 + -5(5t + 1) (-1 * 2 + t * 2) + -3(4t + -3) = 10 + -5(5t + 1) (-2 + 2t) + -3(4t + -3) = 10 + -5(5t + 1) Reorder the terms: -2 + 2t + -3(-3 + 4t) = 10 + -5(5t + 1) -2 + 2t + (-3 * -3 + 4t * -3) = 10 + -5(5t + 1) -2 + 2t + (9 + -12t) = 10 + -5(5t + 1) Reorder the terms: -2 + 9 + 2t + -12t = 10 + -5(5t + 1) Combine like terms: -2 + 9 = 7 7 + 2t + -12t = 10 + -5(5t + 1) Combine like terms: 2t + -12t = -10t 7 + -10t = 10 + -5(5t + 1) Reorder the terms: 7 + -10t = 10 + -5(1 + 5t) 7 + -10t = 10 + (1 * -5 + 5t * -5) 7 + -10t = 10 + (-5 + -25t) Combine like terms: 10 + -5 = 5 7 + -10t = 5 + -25t Solving 7 + -10t = 5 + -25t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25t' to each side of the equation. 7 + -10t + 25t = 5 + -25t + 25t Combine like terms: -10t + 25t = 15t 7 + 15t = 5 + -25t + 25t Combine like terms: -25t + 25t = 0 7 + 15t = 5 + 0 7 + 15t = 5 Add '-7' to each side of the equation. 7 + -7 + 15t = 5 + -7 Combine like terms: 7 + -7 = 0 0 + 15t = 5 + -7 15t = 5 + -7 Combine like terms: 5 + -7 = -2 15t = -2 Divide each side by '15'. t = -0.1333333333 Simplifying t = -0.1333333333
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