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Simplifying 3(2t + -1) + -2(5t + 1) = 4(3t + 4) Reorder the terms: 3(-1 + 2t) + -2(5t + 1) = 4(3t + 4) (-1 * 3 + 2t * 3) + -2(5t + 1) = 4(3t + 4) (-3 + 6t) + -2(5t + 1) = 4(3t + 4) Reorder the terms: -3 + 6t + -2(1 + 5t) = 4(3t + 4) -3 + 6t + (1 * -2 + 5t * -2) = 4(3t + 4) -3 + 6t + (-2 + -10t) = 4(3t + 4) Reorder the terms: -3 + -2 + 6t + -10t = 4(3t + 4) Combine like terms: -3 + -2 = -5 -5 + 6t + -10t = 4(3t + 4) Combine like terms: 6t + -10t = -4t -5 + -4t = 4(3t + 4) Reorder the terms: -5 + -4t = 4(4 + 3t) -5 + -4t = (4 * 4 + 3t * 4) -5 + -4t = (16 + 12t) Solving -5 + -4t = 16 + 12t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-12t' to each side of the equation. -5 + -4t + -12t = 16 + 12t + -12t Combine like terms: -4t + -12t = -16t -5 + -16t = 16 + 12t + -12t Combine like terms: 12t + -12t = 0 -5 + -16t = 16 + 0 -5 + -16t = 16 Add '5' to each side of the equation. -5 + 5 + -16t = 16 + 5 Combine like terms: -5 + 5 = 0 0 + -16t = 16 + 5 -16t = 16 + 5 Combine like terms: 16 + 5 = 21 -16t = 21 Divide each side by '-16'. t = -1.3125 Simplifying t = -1.3125
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