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Simplifying 2(4t + -2) + 14 = 5(t + -1) + -1(4t + 4) Reorder the terms: 2(-2 + 4t) + 14 = 5(t + -1) + -1(4t + 4) (-2 * 2 + 4t * 2) + 14 = 5(t + -1) + -1(4t + 4) (-4 + 8t) + 14 = 5(t + -1) + -1(4t + 4) Reorder the terms: -4 + 14 + 8t = 5(t + -1) + -1(4t + 4) Combine like terms: -4 + 14 = 10 10 + 8t = 5(t + -1) + -1(4t + 4) Reorder the terms: 10 + 8t = 5(-1 + t) + -1(4t + 4) 10 + 8t = (-1 * 5 + t * 5) + -1(4t + 4) 10 + 8t = (-5 + 5t) + -1(4t + 4) Reorder the terms: 10 + 8t = -5 + 5t + -1(4 + 4t) 10 + 8t = -5 + 5t + (4 * -1 + 4t * -1) 10 + 8t = -5 + 5t + (-4 + -4t) Reorder the terms: 10 + 8t = -5 + -4 + 5t + -4t Combine like terms: -5 + -4 = -9 10 + 8t = -9 + 5t + -4t Combine like terms: 5t + -4t = 1t 10 + 8t = -9 + 1t Solving 10 + 8t = -9 + 1t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1t' to each side of the equation. 10 + 8t + -1t = -9 + 1t + -1t Combine like terms: 8t + -1t = 7t 10 + 7t = -9 + 1t + -1t Combine like terms: 1t + -1t = 0 10 + 7t = -9 + 0 10 + 7t = -9 Add '-10' to each side of the equation. 10 + -10 + 7t = -9 + -10 Combine like terms: 10 + -10 = 0 0 + 7t = -9 + -10 7t = -9 + -10 Combine like terms: -9 + -10 = -19 7t = -19 Divide each side by '7'. t = -2.714285714 Simplifying t = -2.714285714
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