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Simplifying 6(t + 8) + -5(4t + -2) = -15(t + -5) + 2 Reorder the terms: 6(8 + t) + -5(4t + -2) = -15(t + -5) + 2 (8 * 6 + t * 6) + -5(4t + -2) = -15(t + -5) + 2 (48 + 6t) + -5(4t + -2) = -15(t + -5) + 2 Reorder the terms: 48 + 6t + -5(-2 + 4t) = -15(t + -5) + 2 48 + 6t + (-2 * -5 + 4t * -5) = -15(t + -5) + 2 48 + 6t + (10 + -20t) = -15(t + -5) + 2 Reorder the terms: 48 + 10 + 6t + -20t = -15(t + -5) + 2 Combine like terms: 48 + 10 = 58 58 + 6t + -20t = -15(t + -5) + 2 Combine like terms: 6t + -20t = -14t 58 + -14t = -15(t + -5) + 2 Reorder the terms: 58 + -14t = -15(-5 + t) + 2 58 + -14t = (-5 * -15 + t * -15) + 2 58 + -14t = (75 + -15t) + 2 Reorder the terms: 58 + -14t = 75 + 2 + -15t Combine like terms: 75 + 2 = 77 58 + -14t = 77 + -15t Solving 58 + -14t = 77 + -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. 58 + -14t + 15t = 77 + -15t + 15t Combine like terms: -14t + 15t = 1t 58 + 1t = 77 + -15t + 15t Combine like terms: -15t + 15t = 0 58 + 1t = 77 + 0 58 + 1t = 77 Add '-58' to each side of the equation. 58 + -58 + 1t = 77 + -58 Combine like terms: 58 + -58 = 0 0 + 1t = 77 + -58 1t = 77 + -58 Combine like terms: 77 + -58 = 19 1t = 19 Divide each side by '1'. t = 19 Simplifying t = 19
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