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Simplifying 5(3t + -1) + 15 = 4(t + -1) + -1(3t + 4) Reorder the terms: 5(-1 + 3t) + 15 = 4(t + -1) + -1(3t + 4) (-1 * 5 + 3t * 5) + 15 = 4(t + -1) + -1(3t + 4) (-5 + 15t) + 15 = 4(t + -1) + -1(3t + 4) Reorder the terms: -5 + 15 + 15t = 4(t + -1) + -1(3t + 4) Combine like terms: -5 + 15 = 10 10 + 15t = 4(t + -1) + -1(3t + 4) Reorder the terms: 10 + 15t = 4(-1 + t) + -1(3t + 4) 10 + 15t = (-1 * 4 + t * 4) + -1(3t + 4) 10 + 15t = (-4 + 4t) + -1(3t + 4) Reorder the terms: 10 + 15t = -4 + 4t + -1(4 + 3t) 10 + 15t = -4 + 4t + (4 * -1 + 3t * -1) 10 + 15t = -4 + 4t + (-4 + -3t) Reorder the terms: 10 + 15t = -4 + -4 + 4t + -3t Combine like terms: -4 + -4 = -8 10 + 15t = -8 + 4t + -3t Combine like terms: 4t + -3t = 1t 10 + 15t = -8 + 1t Solving 10 + 15t = -8 + 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 + 15t + -1t = -8 + 1t + -1t Combine like terms: 15t + -1t = 14t 10 + 14t = -8 + 1t + -1t Combine like terms: 1t + -1t = 0 10 + 14t = -8 + 0 10 + 14t = -8 Add '-10' to each side of the equation. 10 + -10 + 14t = -8 + -10 Combine like terms: 10 + -10 = 0 0 + 14t = -8 + -10 14t = -8 + -10 Combine like terms: -8 + -10 = -18 14t = -18 Divide each side by '14'. t = -1.285714286 Simplifying t = -1.285714286
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