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Simplifying 5(t + -2) + 5(3t + 7) = 19(t + 3) + -6 Reorder the terms: 5(-2 + t) + 5(3t + 7) = 19(t + 3) + -6 (-2 * 5 + t * 5) + 5(3t + 7) = 19(t + 3) + -6 (-10 + 5t) + 5(3t + 7) = 19(t + 3) + -6 Reorder the terms: -10 + 5t + 5(7 + 3t) = 19(t + 3) + -6 -10 + 5t + (7 * 5 + 3t * 5) = 19(t + 3) + -6 -10 + 5t + (35 + 15t) = 19(t + 3) + -6 Reorder the terms: -10 + 35 + 5t + 15t = 19(t + 3) + -6 Combine like terms: -10 + 35 = 25 25 + 5t + 15t = 19(t + 3) + -6 Combine like terms: 5t + 15t = 20t 25 + 20t = 19(t + 3) + -6 Reorder the terms: 25 + 20t = 19(3 + t) + -6 25 + 20t = (3 * 19 + t * 19) + -6 25 + 20t = (57 + 19t) + -6 Reorder the terms: 25 + 20t = 57 + -6 + 19t Combine like terms: 57 + -6 = 51 25 + 20t = 51 + 19t Solving 25 + 20t = 51 + 19t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-19t' to each side of the equation. 25 + 20t + -19t = 51 + 19t + -19t Combine like terms: 20t + -19t = 1t 25 + 1t = 51 + 19t + -19t Combine like terms: 19t + -19t = 0 25 + 1t = 51 + 0 25 + 1t = 51 Add '-25' to each side of the equation. 25 + -25 + 1t = 51 + -25 Combine like terms: 25 + -25 = 0 0 + 1t = 51 + -25 1t = 51 + -25 Combine like terms: 51 + -25 = 26 1t = 26 Divide each side by '1'. t = 26 Simplifying t = 26
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