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Simplifying 2(t + -3) + -3(2t + -1) = 9 + -5(4t + 3) Reorder the terms: 2(-3 + t) + -3(2t + -1) = 9 + -5(4t + 3) (-3 * 2 + t * 2) + -3(2t + -1) = 9 + -5(4t + 3) (-6 + 2t) + -3(2t + -1) = 9 + -5(4t + 3) Reorder the terms: -6 + 2t + -3(-1 + 2t) = 9 + -5(4t + 3) -6 + 2t + (-1 * -3 + 2t * -3) = 9 + -5(4t + 3) -6 + 2t + (3 + -6t) = 9 + -5(4t + 3) Reorder the terms: -6 + 3 + 2t + -6t = 9 + -5(4t + 3) Combine like terms: -6 + 3 = -3 -3 + 2t + -6t = 9 + -5(4t + 3) Combine like terms: 2t + -6t = -4t -3 + -4t = 9 + -5(4t + 3) Reorder the terms: -3 + -4t = 9 + -5(3 + 4t) -3 + -4t = 9 + (3 * -5 + 4t * -5) -3 + -4t = 9 + (-15 + -20t) Combine like terms: 9 + -15 = -6 -3 + -4t = -6 + -20t Solving -3 + -4t = -6 + -20t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20t' to each side of the equation. -3 + -4t + 20t = -6 + -20t + 20t Combine like terms: -4t + 20t = 16t -3 + 16t = -6 + -20t + 20t Combine like terms: -20t + 20t = 0 -3 + 16t = -6 + 0 -3 + 16t = -6 Add '3' to each side of the equation. -3 + 3 + 16t = -6 + 3 Combine like terms: -3 + 3 = 0 0 + 16t = -6 + 3 16t = -6 + 3 Combine like terms: -6 + 3 = -3 16t = -3 Divide each side by '16'. t = -0.1875 Simplifying t = -0.1875
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