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Simplifying 5(t + -8) + 2(2t + 7) = 8(t + -1) + -2 Reorder the terms: 5(-8 + t) + 2(2t + 7) = 8(t + -1) + -2 (-8 * 5 + t * 5) + 2(2t + 7) = 8(t + -1) + -2 (-40 + 5t) + 2(2t + 7) = 8(t + -1) + -2 Reorder the terms: -40 + 5t + 2(7 + 2t) = 8(t + -1) + -2 -40 + 5t + (7 * 2 + 2t * 2) = 8(t + -1) + -2 -40 + 5t + (14 + 4t) = 8(t + -1) + -2 Reorder the terms: -40 + 14 + 5t + 4t = 8(t + -1) + -2 Combine like terms: -40 + 14 = -26 -26 + 5t + 4t = 8(t + -1) + -2 Combine like terms: 5t + 4t = 9t -26 + 9t = 8(t + -1) + -2 Reorder the terms: -26 + 9t = 8(-1 + t) + -2 -26 + 9t = (-1 * 8 + t * 8) + -2 -26 + 9t = (-8 + 8t) + -2 Reorder the terms: -26 + 9t = -8 + -2 + 8t Combine like terms: -8 + -2 = -10 -26 + 9t = -10 + 8t Solving -26 + 9t = -10 + 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. -26 + 9t + -8t = -10 + 8t + -8t Combine like terms: 9t + -8t = 1t -26 + 1t = -10 + 8t + -8t Combine like terms: 8t + -8t = 0 -26 + 1t = -10 + 0 -26 + 1t = -10 Add '26' to each side of the equation. -26 + 26 + 1t = -10 + 26 Combine like terms: -26 + 26 = 0 0 + 1t = -10 + 26 1t = -10 + 26 Combine like terms: -10 + 26 = 16 1t = 16 Divide each side by '1'. t = 16 Simplifying t = 16
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