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Simplifying 5(t + 19) + 10 = 6(t + 9) + -4t Reorder the terms: 5(19 + t) + 10 = 6(t + 9) + -4t (19 * 5 + t * 5) + 10 = 6(t + 9) + -4t (95 + 5t) + 10 = 6(t + 9) + -4t Reorder the terms: 95 + 10 + 5t = 6(t + 9) + -4t Combine like terms: 95 + 10 = 105 105 + 5t = 6(t + 9) + -4t Reorder the terms: 105 + 5t = 6(9 + t) + -4t 105 + 5t = (9 * 6 + t * 6) + -4t 105 + 5t = (54 + 6t) + -4t Combine like terms: 6t + -4t = 2t 105 + 5t = 54 + 2t Solving 105 + 5t = 54 + 2t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2t' to each side of the equation. 105 + 5t + -2t = 54 + 2t + -2t Combine like terms: 5t + -2t = 3t 105 + 3t = 54 + 2t + -2t Combine like terms: 2t + -2t = 0 105 + 3t = 54 + 0 105 + 3t = 54 Add '-105' to each side of the equation. 105 + -105 + 3t = 54 + -105 Combine like terms: 105 + -105 = 0 0 + 3t = 54 + -105 3t = 54 + -105 Combine like terms: 54 + -105 = -51 3t = -51 Divide each side by '3'. t = -17 Simplifying t = -17
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