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Simplifying 3(t + -6) + -5(2t + -7) = 19 + -8(3t + 2) Reorder the terms: 3(-6 + t) + -5(2t + -7) = 19 + -8(3t + 2) (-6 * 3 + t * 3) + -5(2t + -7) = 19 + -8(3t + 2) (-18 + 3t) + -5(2t + -7) = 19 + -8(3t + 2) Reorder the terms: -18 + 3t + -5(-7 + 2t) = 19 + -8(3t + 2) -18 + 3t + (-7 * -5 + 2t * -5) = 19 + -8(3t + 2) -18 + 3t + (35 + -10t) = 19 + -8(3t + 2) Reorder the terms: -18 + 35 + 3t + -10t = 19 + -8(3t + 2) Combine like terms: -18 + 35 = 17 17 + 3t + -10t = 19 + -8(3t + 2) Combine like terms: 3t + -10t = -7t 17 + -7t = 19 + -8(3t + 2) Reorder the terms: 17 + -7t = 19 + -8(2 + 3t) 17 + -7t = 19 + (2 * -8 + 3t * -8) 17 + -7t = 19 + (-16 + -24t) Combine like terms: 19 + -16 = 3 17 + -7t = 3 + -24t Solving 17 + -7t = 3 + -24t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '24t' to each side of the equation. 17 + -7t + 24t = 3 + -24t + 24t Combine like terms: -7t + 24t = 17t 17 + 17t = 3 + -24t + 24t Combine like terms: -24t + 24t = 0 17 + 17t = 3 + 0 17 + 17t = 3 Add '-17' to each side of the equation. 17 + -17 + 17t = 3 + -17 Combine like terms: 17 + -17 = 0 0 + 17t = 3 + -17 17t = 3 + -17 Combine like terms: 3 + -17 = -14 17t = -14 Divide each side by '17'. t = -0.8235294118 Simplifying t = -0.8235294118
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