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Simplifying -5(t + 1) + -1t + -8 = 6(t + 5) + 31 Reorder the terms: -5(1 + t) + -1t + -8 = 6(t + 5) + 31 (1 * -5 + t * -5) + -1t + -8 = 6(t + 5) + 31 (-5 + -5t) + -1t + -8 = 6(t + 5) + 31 Reorder the terms: -5 + -8 + -5t + -1t = 6(t + 5) + 31 Combine like terms: -5 + -8 = -13 -13 + -5t + -1t = 6(t + 5) + 31 Combine like terms: -5t + -1t = -6t -13 + -6t = 6(t + 5) + 31 Reorder the terms: -13 + -6t = 6(5 + t) + 31 -13 + -6t = (5 * 6 + t * 6) + 31 -13 + -6t = (30 + 6t) + 31 Reorder the terms: -13 + -6t = 30 + 31 + 6t Combine like terms: 30 + 31 = 61 -13 + -6t = 61 + 6t Solving -13 + -6t = 61 + 6t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6t' to each side of the equation. -13 + -6t + -6t = 61 + 6t + -6t Combine like terms: -6t + -6t = -12t -13 + -12t = 61 + 6t + -6t Combine like terms: 6t + -6t = 0 -13 + -12t = 61 + 0 -13 + -12t = 61 Add '13' to each side of the equation. -13 + 13 + -12t = 61 + 13 Combine like terms: -13 + 13 = 0 0 + -12t = 61 + 13 -12t = 61 + 13 Combine like terms: 61 + 13 = 74 -12t = 74 Divide each side by '-12'. t = -6.166666667 Simplifying t = -6.166666667
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