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Simplifying 2(t + -7) + -3(2t + -3) = 10 + -6(3t + 5) Reorder the terms: 2(-7 + t) + -3(2t + -3) = 10 + -6(3t + 5) (-7 * 2 + t * 2) + -3(2t + -3) = 10 + -6(3t + 5) (-14 + 2t) + -3(2t + -3) = 10 + -6(3t + 5) Reorder the terms: -14 + 2t + -3(-3 + 2t) = 10 + -6(3t + 5) -14 + 2t + (-3 * -3 + 2t * -3) = 10 + -6(3t + 5) -14 + 2t + (9 + -6t) = 10 + -6(3t + 5) Reorder the terms: -14 + 9 + 2t + -6t = 10 + -6(3t + 5) Combine like terms: -14 + 9 = -5 -5 + 2t + -6t = 10 + -6(3t + 5) Combine like terms: 2t + -6t = -4t -5 + -4t = 10 + -6(3t + 5) Reorder the terms: -5 + -4t = 10 + -6(5 + 3t) -5 + -4t = 10 + (5 * -6 + 3t * -6) -5 + -4t = 10 + (-30 + -18t) Combine like terms: 10 + -30 = -20 -5 + -4t = -20 + -18t Solving -5 + -4t = -20 + -18t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18t' to each side of the equation. -5 + -4t + 18t = -20 + -18t + 18t Combine like terms: -4t + 18t = 14t -5 + 14t = -20 + -18t + 18t Combine like terms: -18t + 18t = 0 -5 + 14t = -20 + 0 -5 + 14t = -20 Add '5' to each side of the equation. -5 + 5 + 14t = -20 + 5 Combine like terms: -5 + 5 = 0 0 + 14t = -20 + 5 14t = -20 + 5 Combine like terms: -20 + 5 = -15 14t = -15 Divide each side by '14'. t = -1.071428571 Simplifying t = -1.071428571
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