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Simplifying 2(t + -2) + -3(4t + -5) = 14 + -5(5t + 1) Reorder the terms: 2(-2 + t) + -3(4t + -5) = 14 + -5(5t + 1) (-2 * 2 + t * 2) + -3(4t + -5) = 14 + -5(5t + 1) (-4 + 2t) + -3(4t + -5) = 14 + -5(5t + 1) Reorder the terms: -4 + 2t + -3(-5 + 4t) = 14 + -5(5t + 1) -4 + 2t + (-5 * -3 + 4t * -3) = 14 + -5(5t + 1) -4 + 2t + (15 + -12t) = 14 + -5(5t + 1) Reorder the terms: -4 + 15 + 2t + -12t = 14 + -5(5t + 1) Combine like terms: -4 + 15 = 11 11 + 2t + -12t = 14 + -5(5t + 1) Combine like terms: 2t + -12t = -10t 11 + -10t = 14 + -5(5t + 1) Reorder the terms: 11 + -10t = 14 + -5(1 + 5t) 11 + -10t = 14 + (1 * -5 + 5t * -5) 11 + -10t = 14 + (-5 + -25t) Combine like terms: 14 + -5 = 9 11 + -10t = 9 + -25t Solving 11 + -10t = 9 + -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. 11 + -10t + 25t = 9 + -25t + 25t Combine like terms: -10t + 25t = 15t 11 + 15t = 9 + -25t + 25t Combine like terms: -25t + 25t = 0 11 + 15t = 9 + 0 11 + 15t = 9 Add '-11' to each side of the equation. 11 + -11 + 15t = 9 + -11 Combine like terms: 11 + -11 = 0 0 + 15t = 9 + -11 15t = 9 + -11 Combine like terms: 9 + -11 = -2 15t = -2 Divide each side by '15'. t = -0.1333333333 Simplifying t = -0.1333333333
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