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Simplifying 4(4t + 6) + -1(2t + -3) = -3(3t + -4) + 5 + 10r Reorder the terms: 4(6 + 4t) + -1(2t + -3) = -3(3t + -4) + 5 + 10r (6 * 4 + 4t * 4) + -1(2t + -3) = -3(3t + -4) + 5 + 10r (24 + 16t) + -1(2t + -3) = -3(3t + -4) + 5 + 10r Reorder the terms: 24 + 16t + -1(-3 + 2t) = -3(3t + -4) + 5 + 10r 24 + 16t + (-3 * -1 + 2t * -1) = -3(3t + -4) + 5 + 10r 24 + 16t + (3 + -2t) = -3(3t + -4) + 5 + 10r Reorder the terms: 24 + 3 + 16t + -2t = -3(3t + -4) + 5 + 10r Combine like terms: 24 + 3 = 27 27 + 16t + -2t = -3(3t + -4) + 5 + 10r Combine like terms: 16t + -2t = 14t 27 + 14t = -3(3t + -4) + 5 + 10r Reorder the terms: 27 + 14t = -3(-4 + 3t) + 5 + 10r 27 + 14t = (-4 * -3 + 3t * -3) + 5 + 10r 27 + 14t = (12 + -9t) + 5 + 10r Reorder the terms: 27 + 14t = 12 + 5 + 10r + -9t Combine like terms: 12 + 5 = 17 27 + 14t = 17 + 10r + -9t Solving 27 + 14t = 17 + 10r + -9t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9t' to each side of the equation. 27 + 14t + 9t = 17 + 10r + -9t + 9t Combine like terms: 14t + 9t = 23t 27 + 23t = 17 + 10r + -9t + 9t Combine like terms: -9t + 9t = 0 27 + 23t = 17 + 10r + 0 27 + 23t = 17 + 10r Add '-27' to each side of the equation. 27 + -27 + 23t = 17 + -27 + 10r Combine like terms: 27 + -27 = 0 0 + 23t = 17 + -27 + 10r 23t = 17 + -27 + 10r Combine like terms: 17 + -27 = -10 23t = -10 + 10r Divide each side by '23'. t = -0.4347826087 + 0.4347826087r Simplifying t = -0.4347826087 + 0.4347826087r
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