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Simplifying 2(t + -2) + -3(5t + -1) = 6 + -5(7t + 4) Reorder the terms: 2(-2 + t) + -3(5t + -1) = 6 + -5(7t + 4) (-2 * 2 + t * 2) + -3(5t + -1) = 6 + -5(7t + 4) (-4 + 2t) + -3(5t + -1) = 6 + -5(7t + 4) Reorder the terms: -4 + 2t + -3(-1 + 5t) = 6 + -5(7t + 4) -4 + 2t + (-1 * -3 + 5t * -3) = 6 + -5(7t + 4) -4 + 2t + (3 + -15t) = 6 + -5(7t + 4) Reorder the terms: -4 + 3 + 2t + -15t = 6 + -5(7t + 4) Combine like terms: -4 + 3 = -1 -1 + 2t + -15t = 6 + -5(7t + 4) Combine like terms: 2t + -15t = -13t -1 + -13t = 6 + -5(7t + 4) Reorder the terms: -1 + -13t = 6 + -5(4 + 7t) -1 + -13t = 6 + (4 * -5 + 7t * -5) -1 + -13t = 6 + (-20 + -35t) Combine like terms: 6 + -20 = -14 -1 + -13t = -14 + -35t Solving -1 + -13t = -14 + -35t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35t' to each side of the equation. -1 + -13t + 35t = -14 + -35t + 35t Combine like terms: -13t + 35t = 22t -1 + 22t = -14 + -35t + 35t Combine like terms: -35t + 35t = 0 -1 + 22t = -14 + 0 -1 + 22t = -14 Add '1' to each side of the equation. -1 + 1 + 22t = -14 + 1 Combine like terms: -1 + 1 = 0 0 + 22t = -14 + 1 22t = -14 + 1 Combine like terms: -14 + 1 = -13 22t = -13 Divide each side by '22'. t = -0.5909090909 Simplifying t = -0.5909090909
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