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Simplifying 4(t + 1) + 5(2 + -5t) = -22(t + -2) + -2 Reorder the terms: 4(1 + t) + 5(2 + -5t) = -22(t + -2) + -2 (1 * 4 + t * 4) + 5(2 + -5t) = -22(t + -2) + -2 (4 + 4t) + 5(2 + -5t) = -22(t + -2) + -2 4 + 4t + (2 * 5 + -5t * 5) = -22(t + -2) + -2 4 + 4t + (10 + -25t) = -22(t + -2) + -2 Reorder the terms: 4 + 10 + 4t + -25t = -22(t + -2) + -2 Combine like terms: 4 + 10 = 14 14 + 4t + -25t = -22(t + -2) + -2 Combine like terms: 4t + -25t = -21t 14 + -21t = -22(t + -2) + -2 Reorder the terms: 14 + -21t = -22(-2 + t) + -2 14 + -21t = (-2 * -22 + t * -22) + -2 14 + -21t = (44 + -22t) + -2 Reorder the terms: 14 + -21t = 44 + -2 + -22t Combine like terms: 44 + -2 = 42 14 + -21t = 42 + -22t Solving 14 + -21t = 42 + -22t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '22t' to each side of the equation. 14 + -21t + 22t = 42 + -22t + 22t Combine like terms: -21t + 22t = 1t 14 + 1t = 42 + -22t + 22t Combine like terms: -22t + 22t = 0 14 + 1t = 42 + 0 14 + 1t = 42 Add '-14' to each side of the equation. 14 + -14 + 1t = 42 + -14 Combine like terms: 14 + -14 = 0 0 + 1t = 42 + -14 1t = 42 + -14 Combine like terms: 42 + -14 = 28 1t = 28 Divide each side by '1'. t = 28 Simplifying t = 28
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