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Simplifying 5(t + -6) + 7t = 5(3t + 5) + -10 Reorder the terms: 5(-6 + t) + 7t = 5(3t + 5) + -10 (-6 * 5 + t * 5) + 7t = 5(3t + 5) + -10 (-30 + 5t) + 7t = 5(3t + 5) + -10 Combine like terms: 5t + 7t = 12t -30 + 12t = 5(3t + 5) + -10 Reorder the terms: -30 + 12t = 5(5 + 3t) + -10 -30 + 12t = (5 * 5 + 3t * 5) + -10 -30 + 12t = (25 + 15t) + -10 Reorder the terms: -30 + 12t = 25 + -10 + 15t Combine like terms: 25 + -10 = 15 -30 + 12t = 15 + 15t Solving -30 + 12t = 15 + 15t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-15t' to each side of the equation. -30 + 12t + -15t = 15 + 15t + -15t Combine like terms: 12t + -15t = -3t -30 + -3t = 15 + 15t + -15t Combine like terms: 15t + -15t = 0 -30 + -3t = 15 + 0 -30 + -3t = 15 Add '30' to each side of the equation. -30 + 30 + -3t = 15 + 30 Combine like terms: -30 + 30 = 0 0 + -3t = 15 + 30 -3t = 15 + 30 Combine like terms: 15 + 30 = 45 -3t = 45 Divide each side by '-3'. t = -15 Simplifying t = -15
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