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Simplifying 2(t + -4) + -3(2t + -5) = 10 + -5(3t + 1) Reorder the terms: 2(-4 + t) + -3(2t + -5) = 10 + -5(3t + 1) (-4 * 2 + t * 2) + -3(2t + -5) = 10 + -5(3t + 1) (-8 + 2t) + -3(2t + -5) = 10 + -5(3t + 1) Reorder the terms: -8 + 2t + -3(-5 + 2t) = 10 + -5(3t + 1) -8 + 2t + (-5 * -3 + 2t * -3) = 10 + -5(3t + 1) -8 + 2t + (15 + -6t) = 10 + -5(3t + 1) Reorder the terms: -8 + 15 + 2t + -6t = 10 + -5(3t + 1) Combine like terms: -8 + 15 = 7 7 + 2t + -6t = 10 + -5(3t + 1) Combine like terms: 2t + -6t = -4t 7 + -4t = 10 + -5(3t + 1) Reorder the terms: 7 + -4t = 10 + -5(1 + 3t) 7 + -4t = 10 + (1 * -5 + 3t * -5) 7 + -4t = 10 + (-5 + -15t) Combine like terms: 10 + -5 = 5 7 + -4t = 5 + -15t Solving 7 + -4t = 5 + -15t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15t' to each side of the equation. 7 + -4t + 15t = 5 + -15t + 15t Combine like terms: -4t + 15t = 11t 7 + 11t = 5 + -15t + 15t Combine like terms: -15t + 15t = 0 7 + 11t = 5 + 0 7 + 11t = 5 Add '-7' to each side of the equation. 7 + -7 + 11t = 5 + -7 Combine like terms: 7 + -7 = 0 0 + 11t = 5 + -7 11t = 5 + -7 Combine like terms: 5 + -7 = -2 11t = -2 Divide each side by '11'. t = -0.1818181818 Simplifying t = -0.1818181818
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