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Simplifying 3(t + 1) + 4(2 + -6t) = -22(t + -1) + -6 Reorder the terms: 3(1 + t) + 4(2 + -6t) = -22(t + -1) + -6 (1 * 3 + t * 3) + 4(2 + -6t) = -22(t + -1) + -6 (3 + 3t) + 4(2 + -6t) = -22(t + -1) + -6 3 + 3t + (2 * 4 + -6t * 4) = -22(t + -1) + -6 3 + 3t + (8 + -24t) = -22(t + -1) + -6 Reorder the terms: 3 + 8 + 3t + -24t = -22(t + -1) + -6 Combine like terms: 3 + 8 = 11 11 + 3t + -24t = -22(t + -1) + -6 Combine like terms: 3t + -24t = -21t 11 + -21t = -22(t + -1) + -6 Reorder the terms: 11 + -21t = -22(-1 + t) + -6 11 + -21t = (-1 * -22 + t * -22) + -6 11 + -21t = (22 + -22t) + -6 Reorder the terms: 11 + -21t = 22 + -6 + -22t Combine like terms: 22 + -6 = 16 11 + -21t = 16 + -22t Solving 11 + -21t = 16 + -22t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '22t' to each side of the equation. 11 + -21t + 22t = 16 + -22t + 22t Combine like terms: -21t + 22t = 1t 11 + 1t = 16 + -22t + 22t Combine like terms: -22t + 22t = 0 11 + 1t = 16 + 0 11 + 1t = 16 Add '-11' to each side of the equation. 11 + -11 + 1t = 16 + -11 Combine like terms: 11 + -11 = 0 0 + 1t = 16 + -11 1t = 16 + -11 Combine like terms: 16 + -11 = 5 1t = 5 Divide each side by '1'. t = 5 Simplifying t = 5
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