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Simplifying 4(t + -4) + -5(2t + -1) = 14 + -8(3t + 4) Reorder the terms: 4(-4 + t) + -5(2t + -1) = 14 + -8(3t + 4) (-4 * 4 + t * 4) + -5(2t + -1) = 14 + -8(3t + 4) (-16 + 4t) + -5(2t + -1) = 14 + -8(3t + 4) Reorder the terms: -16 + 4t + -5(-1 + 2t) = 14 + -8(3t + 4) -16 + 4t + (-1 * -5 + 2t * -5) = 14 + -8(3t + 4) -16 + 4t + (5 + -10t) = 14 + -8(3t + 4) Reorder the terms: -16 + 5 + 4t + -10t = 14 + -8(3t + 4) Combine like terms: -16 + 5 = -11 -11 + 4t + -10t = 14 + -8(3t + 4) Combine like terms: 4t + -10t = -6t -11 + -6t = 14 + -8(3t + 4) Reorder the terms: -11 + -6t = 14 + -8(4 + 3t) -11 + -6t = 14 + (4 * -8 + 3t * -8) -11 + -6t = 14 + (-32 + -24t) Combine like terms: 14 + -32 = -18 -11 + -6t = -18 + -24t Solving -11 + -6t = -18 + -24t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '24t' to each side of the equation. -11 + -6t + 24t = -18 + -24t + 24t Combine like terms: -6t + 24t = 18t -11 + 18t = -18 + -24t + 24t Combine like terms: -24t + 24t = 0 -11 + 18t = -18 + 0 -11 + 18t = -18 Add '11' to each side of the equation. -11 + 11 + 18t = -18 + 11 Combine like terms: -11 + 11 = 0 0 + 18t = -18 + 11 18t = -18 + 11 Combine like terms: -18 + 11 = -7 18t = -7 Divide each side by '18'. t = -0.3888888889 Simplifying t = -0.3888888889
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