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Simplifying 3(5t + -3) + -4(2t + 1) = 5t + -2 Reorder the terms: 3(-3 + 5t) + -4(2t + 1) = 5t + -2 (-3 * 3 + 5t * 3) + -4(2t + 1) = 5t + -2 (-9 + 15t) + -4(2t + 1) = 5t + -2 Reorder the terms: -9 + 15t + -4(1 + 2t) = 5t + -2 -9 + 15t + (1 * -4 + 2t * -4) = 5t + -2 -9 + 15t + (-4 + -8t) = 5t + -2 Reorder the terms: -9 + -4 + 15t + -8t = 5t + -2 Combine like terms: -9 + -4 = -13 -13 + 15t + -8t = 5t + -2 Combine like terms: 15t + -8t = 7t -13 + 7t = 5t + -2 Reorder the terms: -13 + 7t = -2 + 5t Solving -13 + 7t = -2 + 5t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5t' to each side of the equation. -13 + 7t + -5t = -2 + 5t + -5t Combine like terms: 7t + -5t = 2t -13 + 2t = -2 + 5t + -5t Combine like terms: 5t + -5t = 0 -13 + 2t = -2 + 0 -13 + 2t = -2 Add '13' to each side of the equation. -13 + 13 + 2t = -2 + 13 Combine like terms: -13 + 13 = 0 0 + 2t = -2 + 13 2t = -2 + 13 Combine like terms: -2 + 13 = 11 2t = 11 Divide each side by '2'. t = 5.5 Simplifying t = 5.5
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