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Simplifying 5(-1t + 6) + -3(4t + -2) = 2t + 6 + -5t Reorder the terms: 5(6 + -1t) + -3(4t + -2) = 2t + 6 + -5t (6 * 5 + -1t * 5) + -3(4t + -2) = 2t + 6 + -5t (30 + -5t) + -3(4t + -2) = 2t + 6 + -5t Reorder the terms: 30 + -5t + -3(-2 + 4t) = 2t + 6 + -5t 30 + -5t + (-2 * -3 + 4t * -3) = 2t + 6 + -5t 30 + -5t + (6 + -12t) = 2t + 6 + -5t Reorder the terms: 30 + 6 + -5t + -12t = 2t + 6 + -5t Combine like terms: 30 + 6 = 36 36 + -5t + -12t = 2t + 6 + -5t Combine like terms: -5t + -12t = -17t 36 + -17t = 2t + 6 + -5t Reorder the terms: 36 + -17t = 6 + 2t + -5t Combine like terms: 2t + -5t = -3t 36 + -17t = 6 + -3t Solving 36 + -17t = 6 + -3t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3t' to each side of the equation. 36 + -17t + 3t = 6 + -3t + 3t Combine like terms: -17t + 3t = -14t 36 + -14t = 6 + -3t + 3t Combine like terms: -3t + 3t = 0 36 + -14t = 6 + 0 36 + -14t = 6 Add '-36' to each side of the equation. 36 + -36 + -14t = 6 + -36 Combine like terms: 36 + -36 = 0 0 + -14t = 6 + -36 -14t = 6 + -36 Combine like terms: 6 + -36 = -30 -14t = -30 Divide each side by '-14'. t = 2.142857143 Simplifying t = 2.142857143
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