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Simplifying -1(t + 7) + -1(2 + -1t) = 3(t + 5) + -5(4 + -1t) Reorder the terms: -1(7 + t) + -1(2 + -1t) = 3(t + 5) + -5(4 + -1t) (7 * -1 + t * -1) + -1(2 + -1t) = 3(t + 5) + -5(4 + -1t) (-7 + -1t) + -1(2 + -1t) = 3(t + 5) + -5(4 + -1t) -7 + -1t + (2 * -1 + -1t * -1) = 3(t + 5) + -5(4 + -1t) -7 + -1t + (-2 + 1t) = 3(t + 5) + -5(4 + -1t) Reorder the terms: -7 + -2 + -1t + 1t = 3(t + 5) + -5(4 + -1t) Combine like terms: -7 + -2 = -9 -9 + -1t + 1t = 3(t + 5) + -5(4 + -1t) Combine like terms: -1t + 1t = 0 -9 + 0 = 3(t + 5) + -5(4 + -1t) -9 = 3(t + 5) + -5(4 + -1t) Reorder the terms: -9 = 3(5 + t) + -5(4 + -1t) -9 = (5 * 3 + t * 3) + -5(4 + -1t) -9 = (15 + 3t) + -5(4 + -1t) -9 = 15 + 3t + (4 * -5 + -1t * -5) -9 = 15 + 3t + (-20 + 5t) Reorder the terms: -9 = 15 + -20 + 3t + 5t Combine like terms: 15 + -20 = -5 -9 = -5 + 3t + 5t Combine like terms: 3t + 5t = 8t -9 = -5 + 8t Solving -9 = -5 + 8t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8t' to each side of the equation. -9 + -8t = -5 + 8t + -8t Combine like terms: 8t + -8t = 0 -9 + -8t = -5 + 0 -9 + -8t = -5 Add '9' to each side of the equation. -9 + 9 + -8t = -5 + 9 Combine like terms: -9 + 9 = 0 0 + -8t = -5 + 9 -8t = -5 + 9 Combine like terms: -5 + 9 = 4 -8t = 4 Divide each side by '-8'. t = -0.5 Simplifying t = -0.5
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