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Simplifying 7[t + -3] + 1 = 3[t + 4] Reorder the terms: 7[-3 + t] + 1 = 3[t + 4] [-3 * 7 + t * 7] + 1 = 3[t + 4] [-21 + 7t] + 1 = 3[t + 4] Reorder the terms: -21 + 1 + 7t = 3[t + 4] Combine like terms: -21 + 1 = -20 -20 + 7t = 3[t + 4] Reorder the terms: -20 + 7t = 3[4 + t] -20 + 7t = [4 * 3 + t * 3] -20 + 7t = [12 + 3t] Solving -20 + 7t = 12 + 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. -20 + 7t + -3t = 12 + 3t + -3t Combine like terms: 7t + -3t = 4t -20 + 4t = 12 + 3t + -3t Combine like terms: 3t + -3t = 0 -20 + 4t = 12 + 0 -20 + 4t = 12 Add '20' to each side of the equation. -20 + 20 + 4t = 12 + 20 Combine like terms: -20 + 20 = 0 0 + 4t = 12 + 20 4t = 12 + 20 Combine like terms: 12 + 20 = 32 4t = 32 Divide each side by '4'. t = 8 Simplifying t = 8
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