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Simplifying 9 + 6(t + -9) = 4(t + 7) + 9 Reorder the terms: 9 + 6(-9 + t) = 4(t + 7) + 9 9 + (-9 * 6 + t * 6) = 4(t + 7) + 9 9 + (-54 + 6t) = 4(t + 7) + 9 Combine like terms: 9 + -54 = -45 -45 + 6t = 4(t + 7) + 9 Reorder the terms: -45 + 6t = 4(7 + t) + 9 -45 + 6t = (7 * 4 + t * 4) + 9 -45 + 6t = (28 + 4t) + 9 Reorder the terms: -45 + 6t = 28 + 9 + 4t Combine like terms: 28 + 9 = 37 -45 + 6t = 37 + 4t Solving -45 + 6t = 37 + 4t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4t' to each side of the equation. -45 + 6t + -4t = 37 + 4t + -4t Combine like terms: 6t + -4t = 2t -45 + 2t = 37 + 4t + -4t Combine like terms: 4t + -4t = 0 -45 + 2t = 37 + 0 -45 + 2t = 37 Add '45' to each side of the equation. -45 + 45 + 2t = 37 + 45 Combine like terms: -45 + 45 = 0 0 + 2t = 37 + 45 2t = 37 + 45 Combine like terms: 37 + 45 = 82 2t = 82 Divide each side by '2'. t = 41 Simplifying t = 41
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