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Simplifying 3 + 5(t + 6) = 31 + -4(5t + 12) Reorder the terms: 3 + 5(6 + t) = 31 + -4(5t + 12) 3 + (6 * 5 + t * 5) = 31 + -4(5t + 12) 3 + (30 + 5t) = 31 + -4(5t + 12) Combine like terms: 3 + 30 = 33 33 + 5t = 31 + -4(5t + 12) Reorder the terms: 33 + 5t = 31 + -4(12 + 5t) 33 + 5t = 31 + (12 * -4 + 5t * -4) 33 + 5t = 31 + (-48 + -20t) Combine like terms: 31 + -48 = -17 33 + 5t = -17 + -20t Solving 33 + 5t = -17 + -20t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20t' to each side of the equation. 33 + 5t + 20t = -17 + -20t + 20t Combine like terms: 5t + 20t = 25t 33 + 25t = -17 + -20t + 20t Combine like terms: -20t + 20t = 0 33 + 25t = -17 + 0 33 + 25t = -17 Add '-33' to each side of the equation. 33 + -33 + 25t = -17 + -33 Combine like terms: 33 + -33 = 0 0 + 25t = -17 + -33 25t = -17 + -33 Combine like terms: -17 + -33 = -50 25t = -50 Divide each side by '25'. t = -2 Simplifying t = -2
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