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Simplifying 6(t + 3) + -8(-9t + -8) = 77(t + 1) + -4 Reorder the terms: 6(3 + t) + -8(-9t + -8) = 77(t + 1) + -4 (3 * 6 + t * 6) + -8(-9t + -8) = 77(t + 1) + -4 (18 + 6t) + -8(-9t + -8) = 77(t + 1) + -4 Reorder the terms: 18 + 6t + -8(-8 + -9t) = 77(t + 1) + -4 18 + 6t + (-8 * -8 + -9t * -8) = 77(t + 1) + -4 18 + 6t + (64 + 72t) = 77(t + 1) + -4 Reorder the terms: 18 + 64 + 6t + 72t = 77(t + 1) + -4 Combine like terms: 18 + 64 = 82 82 + 6t + 72t = 77(t + 1) + -4 Combine like terms: 6t + 72t = 78t 82 + 78t = 77(t + 1) + -4 Reorder the terms: 82 + 78t = 77(1 + t) + -4 82 + 78t = (1 * 77 + t * 77) + -4 82 + 78t = (77 + 77t) + -4 Reorder the terms: 82 + 78t = 77 + -4 + 77t Combine like terms: 77 + -4 = 73 82 + 78t = 73 + 77t Solving 82 + 78t = 73 + 77t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-77t' to each side of the equation. 82 + 78t + -77t = 73 + 77t + -77t Combine like terms: 78t + -77t = 1t 82 + 1t = 73 + 77t + -77t Combine like terms: 77t + -77t = 0 82 + 1t = 73 + 0 82 + 1t = 73 Add '-82' to each side of the equation. 82 + -82 + 1t = 73 + -82 Combine like terms: 82 + -82 = 0 0 + 1t = 73 + -82 1t = 73 + -82 Combine like terms: 73 + -82 = -9 1t = -9 Divide each side by '1'. t = -9 Simplifying t = -9
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