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Simplifying 3(t + -3) + -5(4t + -1) = 14 + -7(6t + 5) Reorder the terms: 3(-3 + t) + -5(4t + -1) = 14 + -7(6t + 5) (-3 * 3 + t * 3) + -5(4t + -1) = 14 + -7(6t + 5) (-9 + 3t) + -5(4t + -1) = 14 + -7(6t + 5) Reorder the terms: -9 + 3t + -5(-1 + 4t) = 14 + -7(6t + 5) -9 + 3t + (-1 * -5 + 4t * -5) = 14 + -7(6t + 5) -9 + 3t + (5 + -20t) = 14 + -7(6t + 5) Reorder the terms: -9 + 5 + 3t + -20t = 14 + -7(6t + 5) Combine like terms: -9 + 5 = -4 -4 + 3t + -20t = 14 + -7(6t + 5) Combine like terms: 3t + -20t = -17t -4 + -17t = 14 + -7(6t + 5) Reorder the terms: -4 + -17t = 14 + -7(5 + 6t) -4 + -17t = 14 + (5 * -7 + 6t * -7) -4 + -17t = 14 + (-35 + -42t) Combine like terms: 14 + -35 = -21 -4 + -17t = -21 + -42t Solving -4 + -17t = -21 + -42t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '42t' to each side of the equation. -4 + -17t + 42t = -21 + -42t + 42t Combine like terms: -17t + 42t = 25t -4 + 25t = -21 + -42t + 42t Combine like terms: -42t + 42t = 0 -4 + 25t = -21 + 0 -4 + 25t = -21 Add '4' to each side of the equation. -4 + 4 + 25t = -21 + 4 Combine like terms: -4 + 4 = 0 0 + 25t = -21 + 4 25t = -21 + 4 Combine like terms: -21 + 4 = -17 25t = -17 Divide each side by '25'. t = -0.68 Simplifying t = -0.68
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