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Simplifying 71 = 5(4t + 1) + -3(2t + -4) + -2 Reorder the terms: 71 = 5(1 + 4t) + -3(2t + -4) + -2 71 = (1 * 5 + 4t * 5) + -3(2t + -4) + -2 71 = (5 + 20t) + -3(2t + -4) + -2 Reorder the terms: 71 = 5 + 20t + -3(-4 + 2t) + -2 71 = 5 + 20t + (-4 * -3 + 2t * -3) + -2 71 = 5 + 20t + (12 + -6t) + -2 Reorder the terms: 71 = 5 + 12 + -2 + 20t + -6t Combine like terms: 5 + 12 = 17 71 = 17 + -2 + 20t + -6t Combine like terms: 17 + -2 = 15 71 = 15 + 20t + -6t Combine like terms: 20t + -6t = 14t 71 = 15 + 14t Solving 71 = 15 + 14t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-14t' to each side of the equation. 71 + -14t = 15 + 14t + -14t Combine like terms: 14t + -14t = 0 71 + -14t = 15 + 0 71 + -14t = 15 Add '-71' to each side of the equation. 71 + -71 + -14t = 15 + -71 Combine like terms: 71 + -71 = 0 0 + -14t = 15 + -71 -14t = 15 + -71 Combine like terms: 15 + -71 = -56 -14t = -56 Divide each side by '-14'. t = 4 Simplifying t = 4
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