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Simplifying 2[5 + -2(4 + -1t)] + -7 = 5[2(5t + -3) + 3] + -33 2[5 + (4 * -2 + -1t * -2)] + -7 = 5[2(5t + -3) + 3] + -33 2[5 + (-8 + 2t)] + -7 = 5[2(5t + -3) + 3] + -33 Combine like terms: 5 + -8 = -3 2[-3 + 2t] + -7 = 5[2(5t + -3) + 3] + -33 [-3 * 2 + 2t * 2] + -7 = 5[2(5t + -3) + 3] + -33 [-6 + 4t] + -7 = 5[2(5t + -3) + 3] + -33 Reorder the terms: -6 + -7 + 4t = 5[2(5t + -3) + 3] + -33 Combine like terms: -6 + -7 = -13 -13 + 4t = 5[2(5t + -3) + 3] + -33 Reorder the terms: -13 + 4t = 5[2(-3 + 5t) + 3] + -33 -13 + 4t = 5[(-3 * 2 + 5t * 2) + 3] + -33 -13 + 4t = 5[(-6 + 10t) + 3] + -33 Reorder the terms: -13 + 4t = 5[-6 + 3 + 10t] + -33 Combine like terms: -6 + 3 = -3 -13 + 4t = 5[-3 + 10t] + -33 -13 + 4t = [-3 * 5 + 10t * 5] + -33 -13 + 4t = [-15 + 50t] + -33 Reorder the terms: -13 + 4t = -15 + -33 + 50t Combine like terms: -15 + -33 = -48 -13 + 4t = -48 + 50t Solving -13 + 4t = -48 + 50t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-50t' to each side of the equation. -13 + 4t + -50t = -48 + 50t + -50t Combine like terms: 4t + -50t = -46t -13 + -46t = -48 + 50t + -50t Combine like terms: 50t + -50t = 0 -13 + -46t = -48 + 0 -13 + -46t = -48 Add '13' to each side of the equation. -13 + 13 + -46t = -48 + 13 Combine like terms: -13 + 13 = 0 0 + -46t = -48 + 13 -46t = -48 + 13 Combine like terms: -48 + 13 = -35 -46t = -35 Divide each side by '-46'. t = 0.7608695652 Simplifying t = 0.7608695652
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