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Simplifying 2(t + -3) + -3(2t + -1) = 17 + -5(3t + 5) Reorder the terms: 2(-3 + t) + -3(2t + -1) = 17 + -5(3t + 5) (-3 * 2 + t * 2) + -3(2t + -1) = 17 + -5(3t + 5) (-6 + 2t) + -3(2t + -1) = 17 + -5(3t + 5) Reorder the terms: -6 + 2t + -3(-1 + 2t) = 17 + -5(3t + 5) -6 + 2t + (-1 * -3 + 2t * -3) = 17 + -5(3t + 5) -6 + 2t + (3 + -6t) = 17 + -5(3t + 5) Reorder the terms: -6 + 3 + 2t + -6t = 17 + -5(3t + 5) Combine like terms: -6 + 3 = -3 -3 + 2t + -6t = 17 + -5(3t + 5) Combine like terms: 2t + -6t = -4t -3 + -4t = 17 + -5(3t + 5) Reorder the terms: -3 + -4t = 17 + -5(5 + 3t) -3 + -4t = 17 + (5 * -5 + 3t * -5) -3 + -4t = 17 + (-25 + -15t) Combine like terms: 17 + -25 = -8 -3 + -4t = -8 + -15t Solving -3 + -4t = -8 + -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. -3 + -4t + 15t = -8 + -15t + 15t Combine like terms: -4t + 15t = 11t -3 + 11t = -8 + -15t + 15t Combine like terms: -15t + 15t = 0 -3 + 11t = -8 + 0 -3 + 11t = -8 Add '3' to each side of the equation. -3 + 3 + 11t = -8 + 3 Combine like terms: -3 + 3 = 0 0 + 11t = -8 + 3 11t = -8 + 3 Combine like terms: -8 + 3 = -5 11t = -5 Divide each side by '11'. t = -0.4545454545 Simplifying t = -0.4545454545
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