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Simplifying 7(t + 3) + 9 = 3(t + -2) + 6 Reorder the terms: 7(3 + t) + 9 = 3(t + -2) + 6 (3 * 7 + t * 7) + 9 = 3(t + -2) + 6 (21 + 7t) + 9 = 3(t + -2) + 6 Reorder the terms: 21 + 9 + 7t = 3(t + -2) + 6 Combine like terms: 21 + 9 = 30 30 + 7t = 3(t + -2) + 6 Reorder the terms: 30 + 7t = 3(-2 + t) + 6 30 + 7t = (-2 * 3 + t * 3) + 6 30 + 7t = (-6 + 3t) + 6 Reorder the terms: 30 + 7t = -6 + 6 + 3t Combine like terms: -6 + 6 = 0 30 + 7t = 0 + 3t 30 + 7t = 3t Solving 30 + 7t = 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. 30 + 7t + -3t = 3t + -3t Combine like terms: 7t + -3t = 4t 30 + 4t = 3t + -3t Combine like terms: 3t + -3t = 0 30 + 4t = 0 Add '-30' to each side of the equation. 30 + -30 + 4t = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 4t = 0 + -30 4t = 0 + -30 Combine like terms: 0 + -30 = -30 4t = -30 Divide each side by '4'. t = -7.5 Simplifying t = -7.5
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