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Simplifying 5(2t + -1) + 3(3t + 4) = 4(4t + 7) Reorder the terms: 5(-1 + 2t) + 3(3t + 4) = 4(4t + 7) (-1 * 5 + 2t * 5) + 3(3t + 4) = 4(4t + 7) (-5 + 10t) + 3(3t + 4) = 4(4t + 7) Reorder the terms: -5 + 10t + 3(4 + 3t) = 4(4t + 7) -5 + 10t + (4 * 3 + 3t * 3) = 4(4t + 7) -5 + 10t + (12 + 9t) = 4(4t + 7) Reorder the terms: -5 + 12 + 10t + 9t = 4(4t + 7) Combine like terms: -5 + 12 = 7 7 + 10t + 9t = 4(4t + 7) Combine like terms: 10t + 9t = 19t 7 + 19t = 4(4t + 7) Reorder the terms: 7 + 19t = 4(7 + 4t) 7 + 19t = (7 * 4 + 4t * 4) 7 + 19t = (28 + 16t) Solving 7 + 19t = 28 + 16t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-16t' to each side of the equation. 7 + 19t + -16t = 28 + 16t + -16t Combine like terms: 19t + -16t = 3t 7 + 3t = 28 + 16t + -16t Combine like terms: 16t + -16t = 0 7 + 3t = 28 + 0 7 + 3t = 28 Add '-7' to each side of the equation. 7 + -7 + 3t = 28 + -7 Combine like terms: 7 + -7 = 0 0 + 3t = 28 + -7 3t = 28 + -7 Combine like terms: 28 + -7 = 21 3t = 21 Divide each side by '3'. t = 7 Simplifying t = 7
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