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Simplifying 8(2t + -1) + -1(5t + 6) = 5(t + 9) + -5 Reorder the terms: 8(-1 + 2t) + -1(5t + 6) = 5(t + 9) + -5 (-1 * 8 + 2t * 8) + -1(5t + 6) = 5(t + 9) + -5 (-8 + 16t) + -1(5t + 6) = 5(t + 9) + -5 Reorder the terms: -8 + 16t + -1(6 + 5t) = 5(t + 9) + -5 -8 + 16t + (6 * -1 + 5t * -1) = 5(t + 9) + -5 -8 + 16t + (-6 + -5t) = 5(t + 9) + -5 Reorder the terms: -8 + -6 + 16t + -5t = 5(t + 9) + -5 Combine like terms: -8 + -6 = -14 -14 + 16t + -5t = 5(t + 9) + -5 Combine like terms: 16t + -5t = 11t -14 + 11t = 5(t + 9) + -5 Reorder the terms: -14 + 11t = 5(9 + t) + -5 -14 + 11t = (9 * 5 + t * 5) + -5 -14 + 11t = (45 + 5t) + -5 Reorder the terms: -14 + 11t = 45 + -5 + 5t Combine like terms: 45 + -5 = 40 -14 + 11t = 40 + 5t Solving -14 + 11t = 40 + 5t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5t' to each side of the equation. -14 + 11t + -5t = 40 + 5t + -5t Combine like terms: 11t + -5t = 6t -14 + 6t = 40 + 5t + -5t Combine like terms: 5t + -5t = 0 -14 + 6t = 40 + 0 -14 + 6t = 40 Add '14' to each side of the equation. -14 + 14 + 6t = 40 + 14 Combine like terms: -14 + 14 = 0 0 + 6t = 40 + 14 6t = 40 + 14 Combine like terms: 40 + 14 = 54 6t = 54 Divide each side by '6'. t = 9 Simplifying t = 9
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