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Simplifying 3(t + -1) + -4(4t + -3) = 7 + -6(6t + 1) Reorder the terms: 3(-1 + t) + -4(4t + -3) = 7 + -6(6t + 1) (-1 * 3 + t * 3) + -4(4t + -3) = 7 + -6(6t + 1) (-3 + 3t) + -4(4t + -3) = 7 + -6(6t + 1) Reorder the terms: -3 + 3t + -4(-3 + 4t) = 7 + -6(6t + 1) -3 + 3t + (-3 * -4 + 4t * -4) = 7 + -6(6t + 1) -3 + 3t + (12 + -16t) = 7 + -6(6t + 1) Reorder the terms: -3 + 12 + 3t + -16t = 7 + -6(6t + 1) Combine like terms: -3 + 12 = 9 9 + 3t + -16t = 7 + -6(6t + 1) Combine like terms: 3t + -16t = -13t 9 + -13t = 7 + -6(6t + 1) Reorder the terms: 9 + -13t = 7 + -6(1 + 6t) 9 + -13t = 7 + (1 * -6 + 6t * -6) 9 + -13t = 7 + (-6 + -36t) Combine like terms: 7 + -6 = 1 9 + -13t = 1 + -36t Solving 9 + -13t = 1 + -36t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '36t' to each side of the equation. 9 + -13t + 36t = 1 + -36t + 36t Combine like terms: -13t + 36t = 23t 9 + 23t = 1 + -36t + 36t Combine like terms: -36t + 36t = 0 9 + 23t = 1 + 0 9 + 23t = 1 Add '-9' to each side of the equation. 9 + -9 + 23t = 1 + -9 Combine like terms: 9 + -9 = 0 0 + 23t = 1 + -9 23t = 1 + -9 Combine like terms: 1 + -9 = -8 23t = -8 Divide each side by '23'. t = -0.347826087 Simplifying t = -0.347826087
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