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Simplifying 5(t + -3) + -4(2t + -7) = 9 + -8(3t + 2) Reorder the terms: 5(-3 + t) + -4(2t + -7) = 9 + -8(3t + 2) (-3 * 5 + t * 5) + -4(2t + -7) = 9 + -8(3t + 2) (-15 + 5t) + -4(2t + -7) = 9 + -8(3t + 2) Reorder the terms: -15 + 5t + -4(-7 + 2t) = 9 + -8(3t + 2) -15 + 5t + (-7 * -4 + 2t * -4) = 9 + -8(3t + 2) -15 + 5t + (28 + -8t) = 9 + -8(3t + 2) Reorder the terms: -15 + 28 + 5t + -8t = 9 + -8(3t + 2) Combine like terms: -15 + 28 = 13 13 + 5t + -8t = 9 + -8(3t + 2) Combine like terms: 5t + -8t = -3t 13 + -3t = 9 + -8(3t + 2) Reorder the terms: 13 + -3t = 9 + -8(2 + 3t) 13 + -3t = 9 + (2 * -8 + 3t * -8) 13 + -3t = 9 + (-16 + -24t) Combine like terms: 9 + -16 = -7 13 + -3t = -7 + -24t Solving 13 + -3t = -7 + -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. 13 + -3t + 24t = -7 + -24t + 24t Combine like terms: -3t + 24t = 21t 13 + 21t = -7 + -24t + 24t Combine like terms: -24t + 24t = 0 13 + 21t = -7 + 0 13 + 21t = -7 Add '-13' to each side of the equation. 13 + -13 + 21t = -7 + -13 Combine like terms: 13 + -13 = 0 0 + 21t = -7 + -13 21t = -7 + -13 Combine like terms: -7 + -13 = -20 21t = -20 Divide each side by '21'. t = -0.9523809524 Simplifying t = -0.9523809524
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