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Simplifying 4t + 8 + -6(2t + -1) = 3(4t + -3) + -7(t + -2) Reorder the terms: 4t + 8 + -6(-1 + 2t) = 3(4t + -3) + -7(t + -2) 4t + 8 + (-1 * -6 + 2t * -6) = 3(4t + -3) + -7(t + -2) 4t + 8 + (6 + -12t) = 3(4t + -3) + -7(t + -2) Reorder the terms: 8 + 6 + 4t + -12t = 3(4t + -3) + -7(t + -2) Combine like terms: 8 + 6 = 14 14 + 4t + -12t = 3(4t + -3) + -7(t + -2) Combine like terms: 4t + -12t = -8t 14 + -8t = 3(4t + -3) + -7(t + -2) Reorder the terms: 14 + -8t = 3(-3 + 4t) + -7(t + -2) 14 + -8t = (-3 * 3 + 4t * 3) + -7(t + -2) 14 + -8t = (-9 + 12t) + -7(t + -2) Reorder the terms: 14 + -8t = -9 + 12t + -7(-2 + t) 14 + -8t = -9 + 12t + (-2 * -7 + t * -7) 14 + -8t = -9 + 12t + (14 + -7t) Reorder the terms: 14 + -8t = -9 + 14 + 12t + -7t Combine like terms: -9 + 14 = 5 14 + -8t = 5 + 12t + -7t Combine like terms: 12t + -7t = 5t 14 + -8t = 5 + 5t Solving 14 + -8t = 5 + 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. 14 + -8t + -5t = 5 + 5t + -5t Combine like terms: -8t + -5t = -13t 14 + -13t = 5 + 5t + -5t Combine like terms: 5t + -5t = 0 14 + -13t = 5 + 0 14 + -13t = 5 Add '-14' to each side of the equation. 14 + -14 + -13t = 5 + -14 Combine like terms: 14 + -14 = 0 0 + -13t = 5 + -14 -13t = 5 + -14 Combine like terms: 5 + -14 = -9 -13t = -9 Divide each side by '-13'. t = 0.6923076923 Simplifying t = 0.6923076923
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