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Simplifying 3(4 + -1t) + 6 = 6(t + -2) + -2 (4 * 3 + -1t * 3) + 6 = 6(t + -2) + -2 (12 + -3t) + 6 = 6(t + -2) + -2 Reorder the terms: 12 + 6 + -3t = 6(t + -2) + -2 Combine like terms: 12 + 6 = 18 18 + -3t = 6(t + -2) + -2 Reorder the terms: 18 + -3t = 6(-2 + t) + -2 18 + -3t = (-2 * 6 + t * 6) + -2 18 + -3t = (-12 + 6t) + -2 Reorder the terms: 18 + -3t = -12 + -2 + 6t Combine like terms: -12 + -2 = -14 18 + -3t = -14 + 6t Solving 18 + -3t = -14 + 6t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6t' to each side of the equation. 18 + -3t + -6t = -14 + 6t + -6t Combine like terms: -3t + -6t = -9t 18 + -9t = -14 + 6t + -6t Combine like terms: 6t + -6t = 0 18 + -9t = -14 + 0 18 + -9t = -14 Add '-18' to each side of the equation. 18 + -18 + -9t = -14 + -18 Combine like terms: 18 + -18 = 0 0 + -9t = -14 + -18 -9t = -14 + -18 Combine like terms: -14 + -18 = -32 -9t = -32 Divide each side by '-9'. t = 3.555555556 Simplifying t = 3.555555556
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