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Simplifying 4(t + 2) + -3(8 + -6t) = 21(t + -1) + 4 Reorder the terms: 4(2 + t) + -3(8 + -6t) = 21(t + -1) + 4 (2 * 4 + t * 4) + -3(8 + -6t) = 21(t + -1) + 4 (8 + 4t) + -3(8 + -6t) = 21(t + -1) + 4 8 + 4t + (8 * -3 + -6t * -3) = 21(t + -1) + 4 8 + 4t + (-24 + 18t) = 21(t + -1) + 4 Reorder the terms: 8 + -24 + 4t + 18t = 21(t + -1) + 4 Combine like terms: 8 + -24 = -16 -16 + 4t + 18t = 21(t + -1) + 4 Combine like terms: 4t + 18t = 22t -16 + 22t = 21(t + -1) + 4 Reorder the terms: -16 + 22t = 21(-1 + t) + 4 -16 + 22t = (-1 * 21 + t * 21) + 4 -16 + 22t = (-21 + 21t) + 4 Reorder the terms: -16 + 22t = -21 + 4 + 21t Combine like terms: -21 + 4 = -17 -16 + 22t = -17 + 21t Solving -16 + 22t = -17 + 21t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-21t' to each side of the equation. -16 + 22t + -21t = -17 + 21t + -21t Combine like terms: 22t + -21t = 1t -16 + 1t = -17 + 21t + -21t Combine like terms: 21t + -21t = 0 -16 + 1t = -17 + 0 -16 + 1t = -17 Add '16' to each side of the equation. -16 + 16 + 1t = -17 + 16 Combine like terms: -16 + 16 = 0 0 + 1t = -17 + 16 1t = -17 + 16 Combine like terms: -17 + 16 = -1 1t = -1 Divide each side by '1'. t = -1 Simplifying t = -1
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